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Parameters a�ecting inductive displacement sensors
Wilkinson, Michael Richard
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PARAMETERS AFFECTING INDUCTIVE
DISPLACEMENT SENSORS
Michael Richard Wilkinson
2003
Thesis for the Degree of Master of Science
School of Engineering
University of Durham
= 2 JUN 2004
Abstract
An investigation of the limitations of inductive displacement sensors (IDSs) was conducted with
the use of electromagnetic finite element analysis (FEA). A comparison of displacement
sensing technologies highlighted the advantages of IDSs in harsh industrial environments, but
an understanding of the operation of IDSs showed that they are limited by the influence of
target material, width and offset. It was proposed that studying the electromagnetic field around
IDSs could reveal more information than was available from the simple impedance
measurements employed by a commercially available lDS.
A test coil sensor and signal processing system was designed and the result was a reliable
system for measuring the magnetic field around the lDS. Experiments showed that the 1 MHz
field had an amplitude of 5 x 10- 6 T at the base of the lDS and two- and three-dimensional FEA
models were constructed that gave closely matching central field values.
The unreliability of the lDS for different target materials was demonstrated experimentally.
FEA simulations showed that changing target permeability and varying target displacement both
altered the whole field amplitude uniformly. This showed that it was not possible to counteract
the target dependence by monitoring the field with the test coil system in this way. Further FEA
simulations revealed field patterns that changed with target offset. An experiment with the test
coil system confirmed that it was possible to use the change in lobe amplitude to measure the
offset of the target; for example when target displacement d1 = 25 mm and offset Os = 1.2 times
the lDS coil diameter, the distance error was 3.6 %, which corresponded to a normalised test
coil output of 0.54. A similar effect was found from target width FEA simulations. Hence it
was possible to correct the output signal from the lDS coil to counteract the effect of an offset
small target.
Colmtents
Parameters Affecting Inductive Displacement Sensors ................................................................. 1
Abstract. ......................................................................................................................................... 2
Contents ......................................................................................................................................... 3
List of Figures ................................................................................................................................ 5
List of Tables ................................................................................................................................. 8
Declarations ................................................................................................................................... 9
Statement of Copyright ................................................................................................................ I 0
Acknowledgements ..................................................................................................................... I1
Chapter 1 Introduction ............................................................................................................ 12
1.I Non-Contact Spatial Sensors ............................................................................................... I3 1.1.1 Capacitive Sensors .................................................................................................. 13 I .1.2 Optical Sensors ....................................................................................................... 14 1.I.3 Ultrasonic Sensors ................................................................................................... 15 1.1.4 Inductive Sensors .................................................................................................... 16 1.1.5 Comparison of Technologies .................................................................................. I6
I.2 Inductive Displacement Sensor Principles ........................................................................... I7 I.2 .1 IDS Coil Impedance ................................................................................................ 17 1.2.2 The Skin Effect ....................................................................................................... 19
1.3 Inductive Displacement Sensor Applications ...................................................................... 20
1.4 Limitations of IDS ............................................................................................................... 21 1.4.1 Target Material. ....................................................................................................... 21 1.4.2 Target Width ........................................................................................................... 22 1.4.3 Target Offset ........................................................................................................... 22
1.5 Context ................................................................................................................................. 23
1.6 Organisation of the Remainder of this Thesis ...................................................................... 26
Chapter 2 Magnetic Field Measurements ............................................................................... 27
2.1 Magnetic Sensor Technologies ............................................................................................ 27 2.1.1 Low-field Sensors ................................................................................................... 28 2.1.2 Earth's Field Sensors .............................................................................................. 29
2.2 Design Requirements ........................................................................................................... 30
2.3 Magneto-Resistive Sensor ................................................................................................... 32 2.3.1 Amplification Circuit .............................................................................................. 32 2.3 .2 Circuit Testing ........................................................................................................ 34
2.4 Test Coil Sensor ................................................................................................................... 34
2.5 Selection and Refinement of Test Coil ................................................................................ 35 2.5.1 Test Coil Construction ............................................................................................ 36 2.5.2 Test Coil Characterisation ....................................................................................... 37
3
Contents
2.6 Collection of Data ................................................................................................................ 39 2.6.1 Signal Noise ............................................................................................................ 39 2.6.2 Phase-Locking Program .......................................................................................... 41
2.7 Summary .............................................................................................................................. 43
Chapter 3 Finite Element Analysis ......................................................................................... 44
3. 1 Generalised FEA Modelling Process ................................................................................... 44 3 .1. 1 Setting Up the Simulation ...................................................................................... .45 3.1 .2 Impedance Simulation ............................................................................................. 45 3.1.3 Eddy Current Solver ................................................................................................ 48 3.1.4 Solution Criteria and Meshing ................................................................................ 50
3.2 Two-Dimensional PEA ........................................................................................................ 51 3.2. 1 Test Problem ........................................................................................................... 51 3.2.2 Simulation Refinement ........................................................................................... 54 3.2.3 Parametric Test Problem ......................................................................................... 56
3.3 Three-Dimensional PEA ...................................................................................................... 57 3.3.1 Test Problem ........................................................................................................... 57 3.3.2 Simulation refinement ............................................................................................. 60 3.3.3 Parametric Problems ............................................................................................... 61
3.4 General Considerations ........................................................................................................ 63 3.4.1 FEA of Experimental Equipment.. .......................................................................... 63 3.4.2 Edge Effects ............................................................................................................ 65 3.4.3 Extraction of Data ................................................................................................... 66
3.5 Summary .............................................................................................................................. 68
Chapter 4 Inductive Displacement Sensor Limitations .......................................................... 70
4.1 Target Material .................................................................................................................... 70 4.1.1 Characterising the Effect of Target Material .......................................................... 70 4.1.2 FEA Simulations of the Influence of Target Material... .......................................... 72 4.1.3 Target Material Summary ....................................................................................... 77
4.2 Target Offset ........................................................................................................................ 77 4.2.1 Characterising the Effect of Target Offset .............................................................. 77 4.2.2 FEA Simulations of an Offset Target.. .................................................................... 79 4.2.3 Experimental Measurements of an Offset Target ................................................... 82 4.2.4 Target Offset Summary ........................................................................................... 82
4.3 Target Width ........................................................................................................................ 83 4.3 .I Characterising the Effect of Target Width .............................................................. 83 4.3.2 FEA Simulations of the Effect of Target Width ..................................................... 85 4.3.3 Target Width Summary ........................................................................................... 86
4.4 Summary .............................................................................................................................. 86
Chapter 5 Conclusions ............................................................................................................ 88
Appendix I Published Research ............................................................................................ 91
References ................................................................................................................................... 98
4
List of Figures
Figure 1.1. Optical displacement sensors with LEDs and PDs. (a) Linear displacement with a second compensating PD. (b) Angular displacement with two main PDs ............... 14
Figure 1.2. The Physical arrangement of an lDS ......................................................................... 17
Figure 1.3. lDS equivalent circuit. ............................................................................................. 18
Figure 1.4. Variation of eddy current properties with depth in the plane wave case. (a) Eddy current density as a function of depth. (b) Eddy current phase angle as a function of depth .................................................................................................................. 20
Figure 2.1. Comparison of typical magnetic field sensor approximate values. Adapted and updated from [29] .......................................................................................................... 27
Figure 2.2. Magnetoresistive effect: a current,/, flows through a ferromagnetic material and an external magnetic flux, B, causes the magnetisation vector, M, to shift by an angle a .................................................................................................................................. 30
Figure 2.3. Amplification circuit used with the MR sensors. Adapted from [33] ..................... 33
Figure 2.4. Constructed amplification circuit with the MR sensor protruding from the left -hand edge ...................................................................................................................... 33
Figure 2.5. Simple test coil construction .................................................................................... 35
Figure 2.6. Magnetic flux density profile of the lDS coil as measured with the test coil. ......... 36
Figure 2. 7. Different coil designs ............................................................................................... 3 7
Figure 2.8. Optimised test coil design. (a) Side view. (b) Projection view .............................. 37
Figure 2.9. Impedance analysis of the test coil. (a) Impedance phase angle 0. (b) Impedance magnitude IZI ..................................................................................................... 38
Figure 2.1 0. Parallel R, L and C circuit model of test coil. ........................................................ 39
Figure 2.11. Signal recorded from a test coil. (a) Global variations. (b) Local variations .............................................................................................................................. 40
Figure 2.12. Screen-shot from the phase-lock Java application ................................................ .42
Figure 2.13. Result of phase-locking an input signal. ............................................................... .42
Figure 3.1. Equivalent circuit for a two-conductor system ........................................................ .46
Figure 3.2. The axial-symmetric geometry of the lDS sensor coil and centred target. Dimensions given in mm ..................................................................................................... 52
Figure 3.3. The magnetic flux plotted for the two-dimensional test problem. The central lighter portions represent a stronger field than the surrounding darker regions .................................................................................................................................. 53
Figure 3.4. Variation in the magnitude of the z-component of the field, IBzl I tesla, with radius, RI mm, along a line 1 mm below the lDS coil. ....................................................... 54
Figure 3.5. Axial-symmetric geometry of the lDS sensor coil and centred target with the inclusion of a dummy object to improve meshing. Dimensions given in mm .............. 55
5
List of Figures
Figure 3.6. Mesh in the space between the coil and target. (a) The original problem without a dummy object. (b) The problem with a refined mesh inside the dummy object. .......................................... :························································································ 56
Figure 3.7. Magnitude of the z-component of the field, IBzl I tesla, with radius, RI mm, along a line 1 mm below the IDS coil, for a geometry with a meshing dummy object .................................................................................................................................... 56
Figure 3.8. The variation of coil inductance, L, with target displacement, d, ............................. 57
Figure 3.9. Three-dimensional geometry of the IDS coil and non-centred target yz-plane cross-section. Dimensions given in mm .................................................................... 58
Figure 3.1 0. Magnetic flux direction plotted in the yz-plane of the three-dimensional test problem .......................................................................................................................... 59
Figure 3.11. Variation in the magnitude of the z-component of the field, IBzl I tesla, with position y I mm, along a line 1 mm below the IDS coil.. ..................................................... 60
Figure 3.12. Variation in the magnitude of the z-component of the field, IBzl I tesla, with position y I mm, along a line 1 mm below the IDS coil, for a geometry with a meshing dummy object. ....................................................................................................... 61
Figure 3.13. The variation of coil inductance, L, with target displacement, d, for an offset target geometry .......................................................................................................... 63
Figure 3.14. Two-dimensional simulation of the IDS coil and target arrangement with a field-measuring test coil. (a) Magnetic flux plot with stronger field represented by lighter colour. (b) Magnitude of the z-component of the field, IBzl I tesla, with position RI mm, along a line I mm below the IDS coil. ..................................................... 64
Figure 3.15. Two-dimensional simulation of the IDS coil and target arrangement with a plastic target spacer. (a) Magnetic flux plot with stronger field represented by lighter colour. (b) Magnitude of the z-component of the field, IBzl I tesla, with position RI mm, along a line 1 mm below the IDS coil. ..................................................... 65
Figure 3.16. Demonstration of the edge effect on the z-component of the magnetic field around the target. ................................................................................................................. 66
Figure 3.17. Application of the three-dimensional convolution program to the field profile of small-target arrangement. (Solid) raw field. (Dash) Processed field ................. 68
Figure 4.1. Influence of target material on IDS displacement measurements. (Solid) Steel. (Dash) Brass. (Dot) Aluminium. (a) Over the whole measurement range. (b) Close-up to highlight differences ................................................................................... 72
Figure 4.2. Influence of target material on the magnetic field, IBzCz = 3 mm)l. from different target material simulations with d, = 15 mm. R=Omm position is directly below the centre of the IDS coil. (Dash) Steel-1008. (Dot) Nickel. (Solid) Aluminium, copper, brass .................................................................................................... 74
Figure 4.3. Variation in central field value,IBzCr=O, z=3)1. with target displacement, d,. (Dash) Steel-1008. (Dot) Nickel. (Solid) Aluminium, copper, brass ................................. 74
Figure 4.4. Impedance components as a function of target displacement, d,. (Dash) Steel-1 008. (Dot) Nickel. (Solid) Aluminium, copper, brass. (a) Resistance, R. (b) Inductance, L . ................................................................................................................. 7 5
Figure 4.5. Dependence of edge effect on target material demonstrated by the field plotted along a line I mm below the IDS coil. (a) Aluminium. (b) Steel. ......................... 76
6
List of Figures
Figure 4.6. Influence of target offset on IDS output. Normalised IDS output with target offset, Os, at different target displacements, d,. (Solid) d, = 10 mm. (Dash) d, = 20 mm. (Dot) d, = 30 mm ............................................................................................ 78
Figure 4. 7. Field profiles for large offset targets for d, = 10 mm. (Solid) Os = 0 mm. (Dash) Os= 100 mm. (Dot) o., = 100 mm. (Dash dot) Os= 125 mm. (Dash dot dot) 0 5 = 125 mm ......................................................................................................................... 79
Figure 4.8. FEA simulations of offset targets at different target displacements. (a)- (d) d, = 10 mm. (e)- (h) d, = 30 mm ........................................................................................ 81
Figure 4.9. Influence of target offset on coil inductance. (Solid) d, = 10 mm. (Dash) d, = 20 mm. (Dot) d, = 30 mm ............................................................................................ 81
Figure 4.1 0. IDS coil impedance and magnetic field lobe amplitude ford, = 30 mm. (Left, solid) Lobe amplitude. (Right, broken) IDS coil inductance .................................... 82
Figure 4.11. Experimental confirmation of FEA simulation results. (Left, solid) Normalised test coil signal. (Right, broken) IDS distance error. ....................................... 82
Figure 4.12. Influence of target width on the IDS output. .......................................................... 84
Figure 4.13. Influence of target width on the IDS output. (Solid) w, = 2.6. (Dash) w, = 1.4. (Dot) w, = 1.2. (a) Non-linearity introduced with different target widths. (b) Distance measurement error resulting from small target widths .................................... 84
Figure 4.14. FEA simulations of the influence of target width on the magnetic field. (a)- (d) d, = 10 mm. (e)- (h) d, = 20 mm .......................................................................... 86
7
List of Tables
Table 1.1. Example applications for ID Ss .................................................................................. 21
Table 3.1. Parameters taken by macro from project file name, where d, = target distance, w, = target width, o5 = target offset. ..................................................................................... 62
Table 4.1. Physical properties of some targets investigated ....................................................... 71
Table 4.2. Influence of target material on IDS coil impedance .................................................. 76
8
Declarations
The author confirms that this thesis conforms to the word length prescribed for the degree to
which it is submitted.
No part of the material offered in this thesis has been previously submitted by the author for a
degree in this or any other University.
9
The copyright of this thesis rests with the author. No quotation from it should be published
without prior written consent and information derived from it should be acknowledged.
10
Acknowledgements
The support and continuously optimistic encouragement from my supervisor Sherri Johnstone
has been very much appreciated and has been pivotal to the success of this work. Many thanks
are also extended to Dave Wood for his assistance throughout the project.
11
Chapter 1
Introduction
The sensor industry is a diverse one, yet it is vital to almost all modem manufacturing processes.
Continual sensor research and development is required to meet the needs of industry by
providing innovative solutions to increase reliability and decrease costs. The field encompasses
research into a range of technologies including optical, ultrasonic and biological for functions
such as liquid and gas sensing, displacement measurement, tomography and water quality
monitoring. Industry sectors where applications are found are just as diverse and include the
automotive industry, structural monitoring for civil and aerospace structures, the chemical
industries and the food industry [ 1].
In many industrial locations - for example in steel works and on production lines - the
distance to metallic materials often needs to be measured and monitored. This task can be
difficult when the application environment is dusty, steamy or similarly harsh. Inductive
proximity sensors are appropriate for this type of situation because they rely on electromagnetic
fields that can pass through the intervening medium unaffected. This type of sensor is now
common place in harsh industrial environments, so the exploration of their limitations and
subsequent improvement is an important physical problem.
This thesis summarises research performed in this important area and in this first chapter the
topic is introduced. There are a number of different technologies suitable for non-contact
displacement measurements and here capacitive, optical, ultrasonic and inductive sensors are
discussed (§ 1.1 ). Their applications and relative merits are observed with particular reference
to the harsh industrial environment described above. This gives a justification to the particular
importance of inductive proximity sensors, which are introduced through a discussion of their
operating principles (§ 1.2) and applications (§ 1.3). The basis of this work has been the
investigation of the limitations of these sensors through research into the influence of target
material, offset and width, which are introduced in section § 1.4. The wider context of this
work and its relation to previous research and publications is discussed (§ 1.5) before the
chapter concludes with a discussion of the organisation of the remainder of this thesis (§ 1.6).
12
Chapter 1
1.1 NonaContact Spatial Sensors
There are number of spatial measuring devices that are useful in an industrial context and they
may be classified as proximity, position, displacement, dimension and vibration sensors. Often
a non-contact spatial sensor can operate in a number of these modes depending on how it is
installed. Proximity sensors return an on or off output signal denoting presence (or part
presence) or absence of the target. Position sensors record the location of an object with respect
to a defined reference coordinate. Displacement sensors give the movement from one position
to another in a defined direction. Part specific geometrical measurements can be determined
with dimension sensors. Finally, the amplitude and frequency of targets with oscillatory motion
are commonly measured with a vibration sensor. The advantage of non-contact sensors over
contact-based sensors is that there is no risk of damage to fragile parts and the sensor can be
positioned in a convenient location to avoid interference with the process being measured.
Industrial processes often require the use of these non-contact spatial sensors to monitor the
target objects in a number of applications from robotic positioning systems to quality control.
Such instruments operate using capacitive, optical, ultrasonic or inductive technologies [2] [3].
Each type has its own set of characteristics and the particular sensor used will depend on
considerations such as: the motion and degrees of freedom to be measured e.g. rotational or
linear motion in single or multiple dimensions; the operating environment e.g. temperature,
humidity, dust, vibrations or mechanical shocks; the required measurement range; and the
measurement performance e.g. sensitivity, linearity and accuracy requirements.
1.1.1 Capacitive Sensors
The capacitance of a pair of electrodes is given by the basic formula C = E G where c is the
permittivity of the dielectric and G is a geometrical factor. For a parallel flat plate capacitor
G = A/ d where A is the area of the plates and d is the displacement between them.
Capacitance-based non-contact spatial measuring systems consist of a sensing plate positioned
above a conducting target and a potential difference developed between the two enables
measurement of the capacitance. Such a system can be constructed in a similar manner to a
variable capacitor, whereby the overlap between the plates, and therefore A, changes depending
on the angular position of the target. This gives an angular position sensor. Alternatively, and
more commonly, if the device is assembled such that d changes with the displacement to be
measured, then the result is a simple, but linear, non-contact displacement sensor. Devices can
be constructed to cover a measurement range of about 2.5-250 mm [3].
Capacitive transducers are also sensitive to changes in the material between the sensor plate
and the target; therefore maintaining a constant dielectric permittivity is important. The
13
Chapter 1
dielectric constant of air increases with humidity and is also influenced by other materials such
as dust, dirt, oil etc. in the sensing gap. This affects the capacitance and thus the resulting
distance measurement. Thermal expansion and contraction of sensor components is a further
source of error and this is a substantial problem when measuring or controlling to high
precisions.
1.1.2 Optical Sensors
Light-emitting diodes (LEDs) and photodiodes (PDs) have fast responses to current and light
intensity respectively, which makes them suitable for use in an intensity-based optical
displacement sensor. Figure l.l(a) shows how an LED and a PD can be positioned face on to
each other to measure the distance between them. A second PD can be added to compensate for
ambient illumination levels and LED fluctuations. Alternatively an angular displacement sensor
may be composed from two fixed position PDs and a moveable LED (figure l.l(b)).
Measurement errors are reduced by combining and averaging the signals from the two PDs. To
further reduce the influence of ambient illumination, the incident light may be modulated and
phase-locking signal processing used to decode the signals from the detector.
Compensator PD (fixed position)O
LED Main PD
(fixeld posl~~l-o-n) ______ (p_o_s-it-io~."Fchanges)
Distance measured
(a)
PD (:)xed position)
Angle measured
aD r--1_ __ t \...._.:.:.! = = = - -.. LED (angle changes)
(fixed position)
(b)
Figure 1.1. Optical displacement sensors with LEDs and PDs. (a) Linear displacement with a second compensating PD. (b) Angular displacement with two main PDs.
Other mechanisms, such as that developed by Wang [4], use light reflected from the target to
obtain a displacement measurement. As the reliability of laser diodes has increased, laser-based
systems are now available that also use a reflection mechanism. The radiation from laser diodes
can be of a much higher intensity than ambient light and so background effects are reduced.
However, all optical systems are most obviously limited by the need for a clean measurement
gap; intervening dust, oil, metal filings, etc. will reduce the reliability of the measurement.
14
Chapter 1
1.1.3 Ultrasonic Sensors
The term ultrasonic refers to sounds with frequencies greater than those audible to humans,
which usually incorporates frequencies greater than 20 kHz. Although medical scanners use
frequencies in the range 1 - 20 MHz, ultrasonic spatial sensors typically utilise the range 20 -
200 kHz. Such devices emit a short burst of ultrasonic sound towards a target, which is then
reflected back to the sensor. The time between transmission and reception of the burst gives a
value for the distance between the sensor and the target. This technology is well established and
a wide range of sensors are available which operate at different frequencies and have different
radiation patterns. The resolution of the measurements depends on the wavelength of the sound
emitted by the sensor, but in general, commercial products are available with resolutions in the
range 0.2- 0.7 %of the full scale.
Assuming transmission occurs under adiabatic conditions, the speed of sound, c, is a function
of temperature, T, and varies as
c=~r:r ( 1.1)
where y is the ratio of heat capacities, R is the universal gas constant(= 8.314 J.mol- 1 .K- 1) and
m is the molar mass of the transmission medium. If it is assumed that air is a diatomic ideal gas
(y= X) with a molar mass of 29.0x10- 3 Kg.mol- 1, then at T=273.15K (0°C),
c = 331.1 m.s- 1• For the higher temperature of T = 313.15 K ( 40 °C), the speed is increased to
c = 354.5 m.s- 1• This demonstrates the requirement for effective temperature compensation.
The nature of the medium in which the ultrasonic system is operating must also be taken into
consideration. In a non-dispersive medium- such as air- the frequency has no influence on
the speed of sound and the energy and sound travel at the same speed. In a dispersive medium
- such as water - sound speed is a function of frequency and each frequency component
propagates with its own phase velocity, but the energy travels at the group velocity.
The maximum range of these sensors depends on the attenuation of the sounds waves. In air
the attenuation of the ultrasonic pulse increases with the frequency and for each frequency the
attenuation is a function of humidity. Industrial processes in the sensor environment may
produce background noise in the ultrasonic range. However, in general, this is less likely to be
a problem at higher frequencies. The size and form of the target affects the intensity of the
reflected sound burst. A large flat surface will reflect the whole beam and the received intensity
is equivalent to the intensity at twice the target distance. An example of this type of situation is
15
Chapter I
measuring the level of a large vat of still liquid. When the target is not flat, a reflection
coefficient may be calculated, which can be taken into consideration when selecting the sensor.
1.1.4 [nductive Sensors
There are two main types of inductive displacement sensor (IDS): those with one coil and those
with more than one coil [2]. IDSs with two or more windings generally consist of a
transmission coil and one or more receiver coils. A conducting material positioned between the
coils will result in a change in the flux measured by the receiving loop. The general
configuration is to have two coils facing each other with a conducting bar that is free to move
between them. Thus by moving the conducting bar and monitoring the receiving loop
impedance, a displacement can be determined. This type of sensor has been utilised in a
number of applications for example by Bartoletti et al. [5] who use such a device in a low-noise
accelerometer for the detection of gravitational waves.
The second type of inductive sensor with one coil can be utilised for non-contact
displacement measurements. Such devices generally comprise a main sensor coil from which
distances are measured and an oscillator I demodulator electronic module as shown in figure 1.2.
The output of the system is a voltage that is directly proportional to the distance being measured.
This type of sensor is used widely in the measurement of the distance to conducting targets in
harsh environments because they are not affected by dust, dirt, humidity etc. between the sensor
and target and because they can be enclosed in a protective casing to allow operation at high
temperatures.
1.1.5 Comparison of Technologies
The technologies of capacitance, optical, ultrasonic and inductive displacement sensors have
been discussed and their relative merits and shortcomings offered. In the context of a harsh
industrial environment - where the measurement gap may be inconsistent and contaminated
with particles of dust, oil, etc. -it is apparent that eddy current inductive displacement sensors
are the most useful. Capacitance-based sensors are limited by their dependence on the
permittivity of the dielectric between the sensing plate and the target material. A more detailed
comparison between capacitive and inductive sensors is offered by Welsby [6]. Although laser
based optical displacement sensors offer an increased reliability compared to LED and
photodiode systems, they are still limited by particles in the sensing gap. IDSs are well suited
for harsh environments, but this type of sensor is not without limitation and the work presented
here has focused on these devices and research into improving them.
16
Oscillator and demodulator Voltmeter
;::::~::::::=.::f------- lDS coil in protective housing
Conductive target material
Figure 1.2. The Physical arrangement of an IDS.
1.2 Inductive Displacement Sensor Principles
Chapter 1
Figure 1.2 shows how an alternating current, / 1, passes through the IDS coil to generate an
alternating magnetic field, H 1• When a conducting target is positioned in the field, eddy
currents are generated on the surface and this produces a secondary magnetic field, H2, which
opposes H 1•
1.2.1 IDS Coil Impedance
The equivalent circuit of the IDS system consists of two loops: the IDS coil and the induced
eddy currents in the target. This arrangement is shown in figure 1.3. A change in the current of
loop one results in a change in the flux through that coil. Loop one and loop two are
magnetically coupled and so a potential difference is induced in the target material. The
induced voltage, V2, is proportional to the rate of change of the flux and thus the rate of change
of the current in loop one, / 1, such that
V - M dl! 2-- I2d/ ( 1.2)
where M 12 is the coupling constant between loop one and loop two, called the mutual inductance,
which depends on the geometrical arrangement of the IDS coil and the target. M21 can be used
to quantify the magnetic coupling between loop two and loop one. In general these two mutual
inductances are equal since loop one and loop two may be interchanged without affecting the
mutual inductance. Thus the mutual inductance is
M =MI2 =M2I ( 1.3)
17
Loop I (IDS coil)
Loop 2 (target)
Figure 1.3. lDS equivalent circuit.
Chapter I
Figure 1.3 shows that each loop has an inductance (L 1 and~) and resistance (R 1 and R2). The
potential difference across the sensor coil with a current of angular frequency, w, is given by
Kirchoffs voltage law as
(1.4)
where i = ~ . But for the second loop there is no overall potential difference and so
(1.5)
Combining these two equations gives an expression for the potential difference across the IDS
coil
( 1.6)
from which the IDS coil equivalent impedance can be extracted
(1.7)
This leads to frequency dependent equations for the IDS coil equivalent resistance
(1.8)
and equivalent inductance
(1.9)
18
Chapter 1
1.2.2 The Skin Effect
An important result of the flow of eddy currents in the target material is the skin effect. This is
the tendency of eddy currents to concentrate in the surface of the target closest to the excitation
field. As the frequency of the excitation field increases, the skin effect increases and the
currents become more concentrated at the surface. The effect is also dependent on the target
conductivity and permeability. The amplitudes of the currents decrease exponentially - or
approximately exponentially, depending on the geometry of the material- with depth into the
target. Also with increased depth, the phase difference between the currents at that depth and
the surface currents increases. An explanation of the skin effect is that eddy currents produce a
magnetic field at a greater depth that counteracts the excitation field, thus reducing its ability to
generate eddy currents deeper in the material.
Libby [7] (pages 123-135) shows that in the plane wave case, where a target of infinite extent
is impinged upon by a perpendicular field of infinite extent, the current density Jz, at a depth z,
is given by
(1.10)
where 10 is the surface current density, f is the frequency and f1 and a are the permeability and
conductivity of the target material respectively. For non-magnetic materials the permeability is
that of free space, f1 = flo = 4rr x 10- 7 H.m- 1, otherwise f1 = flo flr where flr is the relative
permeability of the material. A factor called the standard depth of penetration, or skin depth,
can be introduced that is the depth where the current density has decreased to )!; times its value
at the target surface. Therefore ( 1.10) may be written as
(1.11)
where 8 = (;r f flCY rx is the standard depth of penetration. Figure 1.4(a) shows this variation of
eddy current density with depth into the target. The axis of abscissas has the depth relative to
the standard depth of penetration and the axis of ordinates has the current density relative to the
surface current density.
The phase difference in radians, B, between 10 and Jz is given by
z (1.12) =
19
Chapter I
Figure 1.4(b) show a plot of the phase Jag with depth into the target material. The axis of
abscissas has the depth relative to the standard depth of penetration and the axis of ordinates has
the phase difference between lx and 10•
0.8
0 0.6 ...., -....;· 0.4 .
0.2
0 2
(a)
3 4 5 6 z I r5
6
4 "1:1 e -"' 2
0
0 3 4 5 6 z I r5
(b)
Figure 1.4. Variation of eddy current properties with depth in the plane wave case. (a) Eddy current density as a function of depth. (b) Eddy current phase angle as a function of depth.
1.3 Inductive Displacement Sensor Appli.cations
IDSs may be used in a wide variety of applications ranging from simple distance measurement
to vibration alarms. The electromagnetic nature of IDSs means that they are not affected by
dust, humidity, etc. and may be employed in applications where other technologies - such as
ultrasonic sensors -are not appropriate. Some example applications are detailed in table 1.1.
Aknin et al. [8] describe the use of an IDS in the railway industry for the measurement of the
relative lateral displacement of a rail/wheelset or rail/bogie. Specific applications given are:
"the measurement of the track gauge at high speed, the measurement of the yaw angle and
lateral motion of a bogie, and finally the active steering of the railway wheelset". The device
was expected to operate with rain, frost, snow, rapid cooling of the device when entering
tunnels, large acceleration forces and the possibility of one side being heated through sun
exposure and the other remaining cool in shadows. Optical sensors were ruled out because of
mud, chips, metal filing and grease splashes, and capacitive sensors were unfeasible because of
the large displacement that was required to keep the sensor clear of guard rails, level crossings,
etc. Hence an IDS array was found to be the most suitable system.
20
Chapter 1
Table 1.1. Example applications for IDSs.
Application
Alignment
Cylinder diameter
Non-conductive material thickness
Part sorting
Vibration measurement or alert
Description
Two IDSs positioned perpendicularly around a joint can be used to show the position of a metallic rod during an alignment process.
Two IDSs diametrically positioned towards the cylinder (e.g. a shaft) can be used to measure the diameter if the separation of the IDSs is known first.
Place the test material on a conducting base and the ECS on the upper side of the material.
Metallic parts on a conveyor system can be sorted by their height over the surface.
Both the amplitude and frequency of vibrations in a metallic object can be recorded. The maximum frequency will be limited by the response times of the electronics and the operation frequency of the coil.
An inductive proximity sensor is described by Sharp and Pater [9] for use in a nuclear facility
to provide status information on moving machinery. Although this paper refers specifically to
proximity sensors rather than displacement sensors, the same principles are applicable. The
authors describe the benefits of using these sensors in a nuclear facility where the reliability of
remote sensing equipment has important safety implications. Although standard inductive
sensors are generally reliable, when subjected to ionising radiation they can fail at relatively low
and unpredictable total doses. By redesigning the electronic circuit and selecting cables with
appropriate specifications, a sensor with radiation tolerance was developed. The tested sensor
has been manufactured by AEA Technology and has found applications in the thermal oxide
reprocessing plant at Sellafield. Some further applications of IDSs are given towards the end of
this chapter in section § 1.5.
1.4 Limitations of lDS
Eddy current IDS have a number of limitations and it is the purpose of this thesis to discuss
these restrictions on their reliability and applications. Section § 1.2 has introduced the theory of
operation for IDSs, which forms the basis of why target material affects the output of the sensor.
Other factors affecting the reliability of IDS measurements are the target width and target offset.
These factors place important limits on the range of applications in which IDSs can be
employed.
1.4.1 Target Material
Equation ( 1.7) shows that the equivalent impedance, Z, of the sensor coil depends on the
angular frequency, w, and thus the frequency, f, of the current 11• The resistance of the eddy
current path, R2, is a function of the resistivity of the target, p, and inductance of the target
21
Chapter 1
depends on the permeability of the target, Jl. Also, as mentioned in section § 1.2, the mutual
inductance, M, varies with the geometry of the coil and target arrangement and so it is a
function of the target displacement from the IDS coil, d,. Thus Z is a function of all these
factors, i.e.
(1.13)
For eddy current displacement sensors, f. p and J1 must be controlled to give the single variable
function
z = g(d,) (1.14)
The frequency may be controlled by selecting a suitable value at the design stage that will
depend on the target skin depth as described in section § 1.2.2. However, p and J1 are properties
of the target material and vary between, for example, steel and aluminium (see table 4.1). This
target dependence can be a major limitation of an eddy current IDS and in situations where
different targets need to be measured, the IDS needs to be recalibrated each time. Commercial
IDSs are usually optimised for either magnetic or non-magnetic targets and it is difficult to use a
system tuned for non-magnetic materials with a magnetic target. Indeed manufacturers state
that with some smaller sensors it is impossible to use a mismatched target and system as the
electronic circuits are optimised for the specific application.
1.4.2 Target Width
The ratio of target size to sensor coil diameter is an important consideration when selecting an
lDS system. Sensor coils can be either shielded or unshielded depending on the application; the
flux from unshielded sensors tends to extend laterally beyond the coil diameter, whereas the
flux from shielded sensors does not tend to spread out in this way. The linear measuring range
is directly proportional to the sensor coil diameter with unshielded coils having a greater
measuring range than shielded coils. A manufacturer's IDS operation manual [ 1 0] states that
for shielded sensors the target should be a minimum of 1.5-2 times the coil diameter, whereas
for unshielded sensors the target material must be at least 2.5-3 times the coil diameter. Using
an IDS with targets smaller than the specified widths will lead to degradation in linearity and
long-term stability. However a target of size greater than the required minimums does not affect
the system.
1.4.3 Target Offset
The influence of an offset target, that is a target that is displaced laterally relative to the centre
of the IDS coil, is related to that of target width. When a target is offset, it appears to be smaller
22
Chapter I
than the required width on the side which has been moved towards the centre of the coil. This
situation can arise where either the target has moved off-centre or the lDS coil has been
displaced laterally.
1.5 Context
lDS technology is well established and much of the current research is based in the sensor
manufacturing industry. For this reason trade journals can provide a useful insight into the
current market and commercially available technologies. For example, an introduction to these
sensors is presented by Welsby and Hitz [ 11] and the techniques required to design and build an
eddy current lDS are given by Roach [ 12]. Besides this, there are also a number of published
works that detail the modelling and improvement of IDSs, from which principles and theories
can be extracted and applied to the work in this thesis.
The inhomogeneity resulting from different target materials is a major problem although only
a small quantity of research on this matter has been published, such as that presented by Tian et
al. [13] and Wang and Becker [14]. In the Tian et al. paper, the influence of target resistivity
and permeability are investigated, as is the influence of the converting circuits. The work
concludes, " ... the effect of inhomogeneity in non-ferrous targets is much less than that of
ferrous targets. Therefore non-contact displacement eddy current sensors are suited to
applications for the precision measurement of non-ferrous targets." Wang and Becker have
reported on their design of an lDS that gives a displacement that is described as being
"practically independent of the material of the object".
There have been a number of reports of new designs and applications of IDSs, such as
Passeraub et al. [15] who present a system that utilised a flat coil to achieve sub-micrometric
sensitivity.
Research published by Bartoletti et al. [5] details "the design of a proximity inductive sensor".
The aims of the work were to get low dimensions, a fast response to change in target
displacement and low costs. The proximity sensor used flat coils that were constructed from a
spiral design etched on a double-sided copper printed board. The advantage of this cheap
process was that the coils were very thin and could therefore be placed in close proximity to the
target. This was found to lead to greater sensitivity compared to the more usual design that
extends laterally relative to the plane of the coil. The paper gives a qualitative discussion about
the temperature dependence of their sensor, which is relevant to the work in this thesis; although
the Bartoletti et al. descriptions are complicated by the fact tat they have used spiral coils.
23
Chapter I
Macovschi and Poupot have presented a two stage report on their study of variable inductance
transducers as proximity sensors. The first part [ 16] describes the computer simulations of the
magnetic circuits in a coil and target system, which were used to extract magnetic parameters.
The magnetic field, the geometry and position of the coils, the permeability of the magnetic
circuits and targets and the saturation of the magnetic circuits were studied. The simulations
were used to compare two different coil core designs and in the second part [ 17] one of the
designs was selected for experimental investigation. Results were presented for the variation of
coil inductance with a number of parameters including: position and geometry of the coils,
magnetic circuit material, target thickness, coil frequency and some auxiliary construction
elements.
A highly sensitive and compact sensor system utilising 1 mm diameter coils has been
demonstrated by Passeraub [18]. The system also incorporated a new electronic interface that
was surface-mounted onto a PCB to include short leads and a low component count. The result
was a low-noise, high-sensitivity lDS. To demonstrate the system, it was used to control a
stepper motor by detecting a 1 mm hole drilled in a rotating brass disc. This was shown to
permit a well-defined numbering of the motor's steps and hence enabled more control of the
motor.
Much work has been done to utilise eddy current -type sensors to measure profiles and
outlines of metallic objects in a process called electromagnetic tomography. Peyton et al. [19]
present an overview of this method, which includes operating techniques and some examples.
Hardy et al. [20] used an eight by eight array of spiral coils to detect and recognise metallic
objects. Each coil was an eddy current lDS and the 64 elements gave a total sensing area of
320 x 320 mm. The output of the system was a computer image which was used to identify
metallic objects in the sensing range. Fenniri et al. [21] used an eddy current lDS to measure
the distance to a conducting target and then utilised a deconvolution algorithm to extract the
profile of the target surface. The system was only demonstrated for certain targets, although
Fenniri et al. suggest that it could have been employed to make an image of simple-shaped
profiles such as toothed gearings, which would allow for the detection of fractured edges. On
similar lines, Passeraub et al. [22] utilise their highly sensitive small coil IDSs to determine
metallic profile and material information of coins. They demonstrate their system by
highlighting the difference in results from genuine and fake coinage.
Belloir et al. [23] describe a smart flat-coil eddy current sensor for metal tag recognition used
to identify buried pipes. The tags were buried with utility pipes and nine configurations were
used to give a unique identification to the utility type (e.g. water, gas, data cabling, etc.). The
24
Chapter 1
intention was that workers were able to locate and identify pipes without needing to excavate
investigation trenches. Although separate emission and receiving coils were used, this work is
closely related to eddy current IDSs in that the metal tags affected the flux distributions such
that they could be identified remotely. The system was further improved [24] and the authors
state that they have reduced the risk of tag misidentification to nearly zero. This work gives
useful insights into hardware and signal processing considerations for IDSs.
An interesting application of an IDS is to measure the position of diesel engine valves as
presented by Marcic [25]. Previous work had involved fitting a sensor to the valve, which
altered its mass and therefore affected the measurements being taken. However, Marcic's
system uses two coils fitted around the valve that do not interfere with its operation. This is not
an eddy current based IDS, but again the design processes given in the paper are relevant to the
present work.
In Scarr and Zelisse's work [26] an eddy current system is used to measure the thickness of
metallised films. The system relies on the skin effect in the target material to attenuate the
incident flux. Results were obtained using just one coil and this operated in a similar manner to
that described here in section § 1.2 and gave a response to target displacement as well as target
thickness. However Scarr and Zelisse wanted a system that would provide thickness results
independent of the target position. To realise this, two coils were used and the target material
was positioned between them; one coil acted as a transmitter and the other as a receiver. The
authors also describe a system where the two coils are on the same side of the target, with the
receiver wrapped inside the transmitter.
On the subject of modelling magnetic displacement sensors, J ohnstone and Peyton [27]
describe the use of three-dimensional finite element simulations to evaluate the performance of
a magnetic sensor system. The technique of using a quarter-geometry model is described and
compared to the full geometry model. Methods to overcome problems associated with meshing
errors are described and the model results are compared to experimental measurements. The
system described by Johnstone and Peyton is quite different from the IDSs described in this
thesis, although the paper's description of the modelling is useful. Huang et al. [28] have also
used finite element analysis to model a displacement sensor. The paper describes how a three
dimensional model of two coils from a non-contact inductive system was constructed. The
models helped the authors to understand the non-linear nature of the device and assisted in the
optimisation of the design.
In summary, despite IDSs now being off-the-shelf devices, research continues m design
optimisation, miniaturisation and the investigation of new applications. Related work on finite
25
Chapter 1
element analysis provides a useful insight into the techniques required to produce reliable
models of IDSs. There has been some investigation of the limitations of IDSs although these
issues have not been fully resolved and still remain an important area ofresearch.
1.6 Organisation of the Remainder of this Thesis
In this chapter the subject of IDSs has been introduced and compared to other sensor
technologies. The performance of these different sensors in a harsh industrial environment has
been discussed and it is argued that IDSs are most appropriate for measuring distances when the
sensing gap is contaminated with dust, steam or oil, etc. Some general applications of lDS have
been introduced and some specific applications have been given. A discussion of the physics of
lOSs has been given, which not only presented an understanding of their operation, but also
described why they are limited by their dependence on the target material. The other limitations
discussed were the influence of target width and target offset. Finally there was a presentation
of some references to previous published research on the subject of lDS applications and
improvements, which sets this thesis in context.
It has been demonstrated that IDSs measure changes in their coil impedance and use this to
determine the target displacement. It is the total field that affects the impedance and therefore
local variations are neglected. The central contention of this thesis is that the structure of the
field can reveal information that is not available from these simple impedance measurements.
The remainder of this thesis describes research that confirms this hypothesis as axiomatic and
utilises this information to address the current limitations of IDSs. Chapter two describes how
measurements of the lDS magnetic field were made. A number of technologies were
investigated and the most appropriate was selected for use in the subsequent experimental work.
Chapter three shows how finite element analysis simulations were used to model the lDS and
includes a discussion of the merits and applications of two- and three-dimensional schemes.
The fourth chapter shows the results of experimental and practical work on the limitations of
lOSs resulting from target material, target offset and target width. The final chapter forms a
summary of the work and draws conclusions about the practicability of making improvements
to lDS designs.
26
Chapter 2
Magnetic Field Measurements
Magnetic fields are central to the operation of IDSs and in this chapter methods for taking
measurements of these fields are described. Magnetic sensing technology has a broad range in
terms of both field strength and the physics involved; this was researched and the relative merits
of different sensors were compared. An estimate of the field amplitude and frequency was
made, which enabled suitable measurement devices to be identified. The application of both
magneto-resistive and test coil devices was investigated and the most appropriate was selected.
Signals were recorded using a digital oscilloscope and a Java application was developed to
reduce the noise using a phase-locking technique. The result was a system that was appropriate
for the field range and frequency of the IDS and this was subsequently applied to the
experimental work described later in this thesis.
2.1 Magnetic Sensor Technologies
Magnetic Sensor Technology
Search Coil
Flux Gate
Optically Pumped
Nuclear-Precession
SQUID
Hall-Effect
Magnetoresisti ve
Detectable Field IT
10 I~ 10 -~ 10 4
I.~ZL ... ~=-~:~\FC:::~::::;::.
.... ,, __ • ~:..:::. ilk'>.~.'--·
Figure 2.1. Comparison of typical magnetic field sensor approximate values. Adapted and updated from [29].
A variety of devices can be used to detect magnetic fields and the technology involved
determines whether they are classified as low-, medium-, or high-field sensors [30]. Devices
that detect magnetic fields < - 10- 10 T can be described as low-field sensors. Given that the
magnitude of Earth's field is - 5 x 10- 5 T, medium-field sensors which operate in the range
10- 10- 10- 3 T, are referred to as Earth's field sensors. Detectors that measure fields > 10- 3 T
27
Chapter 2
can be labelled as bias magnet field sensors. Figure 2.1 lists some devices and their associated
typical approximate sensing ranges.
2.1.1 Low-field Sensors
It can be seen in figure 2.1 that a variety of low-field sensors exist. Application areas include
measuring the nemo-magnetic fields in the brain and military surveillance equipment. However,
these devices tend to be costly and bulky compared to other magnetic field sensors that are
suitable for detecting stronger fields. It should be noted that the fields that are measured by
these sensors are much less than Earth's field and so careful design choices must be made to
ensure that the field of interest is preserved on the output signal. Some technologies suitable for
measuring in this range are nuclear precession magnetometers, superconducting quantum
interference devices and test coils.
Nuclear-Precession
Nuclear-precession magnetometers generally consist of a hydrogen-rich core surrounded by a
coil. Current is passed through the coil to generate a DC magnetic field that aligns the spinning
protons (hydrogen nuclei) like dipole magnets along the direction of the field. After the coil is
turned off the protons are only subject to the magnetic field that is being measured. This field
causes torque on the spinning nuclei and they precess around the direction of the field.
Consequently a small alternating current is induced in the coil with a frequency equal to that of
the precession. Since the field strength is proportional to the precession frequency, an accurate
value for the magnetic field can be determined. Although this type of device can measure very
low fields, it was deemed impractical for the application in hand. The same is true of optically
pumped and fibre-optic magnetometers.
SQUIDS
Superconducting quantum interference devices (SQUIDs) [31] can detect magnetic fields over
15 orders of magnitude from several teslas to several femto-teslas. First developed in the early
1960s these devices utilise a J osephson junction and until recently required low temperatures to
operate. Low temperature superconducting systems are not well suited to practical use outside
the laboratory because of the sophisticated and ex pensive liquid helium (- 4 K) cryogenics
involved. However with the advent of (relatively) high temperature superconductor thin films
SQUIDs have become more practical for testing purposes since they only require smaller and
cheaper liquid nitrogen cooling (- 77 K). Indeed the use of such high temperature SQUIDs has
been demonstrated for enhancing eddy current non-destructive investigation of metallic
structures [31]. However practical and low cost off-the-shelf SQUID systems are a long way
off.
28
Chapter 2
Test Coils The list in figure 2.1 shows that test coils have a wide sensing range and can be used to measure
low-fields. When a loop of wire is subject to an alternating magnetic field, Faraday's law of
magnetic induction states that the EMF of the loop is equal to the negative of the rate of change
of the magnetic flux through the area enclosed by the loop. For a coil of multiple loops, the
EMF is simply multiplied by the number of turns. This is the basis of search coil magnetic field
sensors. The sensitivity depends on the number of loops, the coil area and the permeability of
the core. Since these devices rely on changing magnetic fields - or moving through one -
they cannot be used to measure static or slow-varying fields.
2.1.2 Earth's Field Sensors
Given their sensing range, sensors m this group are typically used to measure the Earth's
magnetic field. Example applications include using electronic compasses for navigation,
determining the yaw of aircraft and projectiles and measuring variations in the field for road
traffic measurements. Some technologies that fall into this range are fluxgate, magnetoresistive
and Hall-effect sensors.
Fluxgate Fluxgate sensors [32] can be used to measure DC or low frequency AC magnetic fields over the
range 10- 10- 10- 4 T. The usual configuration is called a second harmonic device, which
comprises two coils formed on a common high-permeability core. An alternating current in the
excitation coil periodically saturates the magnetic core and the permeability is modulated. The
second winding is a sensing coil that couples with the excitation coil through the core. The
external measured field also affects the core's permeability and a voltage proportional to the
field strength is induced in the sensing coil at the second harmonic of the excitation frequency.
Although standard fluxgates can detect AC magnetic fields they generally have an upper limit of
- 1 kHz, although recent publications have claimed to have achieved a bandwidth of- 1 MHz.
Hall-Effect A particle of charge, q, moving with a velocity,~. in a magnetic field, !1. is subject to a Lorentz
force
(2.1)
which acts in a direction that is perpendicular to~ and fl. The Hall Effect is the influence of the
Lorentz force in a semiconductor material. A voltage applied across a block of semiconductor
material causes a current to flow. If a magnetic field is applied perpendicularly to the current,
then & will cause the charge carried to be deflected in the third dimension. This results in a
29
Chapter 2
build up of charge and a potential difference is developed across the device in the direction
perpendicular to the applied voltage and measured magnetic field. Hall sensors typically use n
type silicon for low-cost applications although other semiconductors such as InAs and AnSb can
be used where greater frequency response and sensitivity are required. This enables easy
integration with other semiconductor elements to create sensors integrated with controlling and
processing electronics.
Magneto ~resistive
The magnetoresistive effect is the property of a current-carrying ferromagnetic material to
change its resistivity in the presence of an external magnetic field. Such a material is permalloy,
which consists of 80 % nickel and 20 % iron and has a high magnetic permeability. Figure 2.2
shows the influence of an external magnetic field on the magnetisation of a strip of material
such as permalloy. The device is arranged such that when there is no external magnetic flux,
the current flows parallel to the magnetisation vector, M. On the application of an external flux,
f1, perpendicular to the current flow, M will rotate by an angle a., which changes the resistance
by
(2.2)
where R0 and L1R0 are material properties.
!l.
I ~I I
Figure 2.2. Magnetoresistive effect: a current, I, flows through a ferromagnetic material and an external magnetic flux, !l., causes the magnetisation vector, M, to shift by an angle a.
2.2 Design Requirements
To gain an insight into which magnetic sensor technologies are suitable for the task in hand,
values of the field magnitude and frequency were required. Initial investigations with a Hall
probe gaussmeter were unsuccessful; no changes from the background readings were observed
in either AC or DC modes. This was assumed to be because the gaussmeter had either too low a
sensitivity or too slow a frequency response.
30
Chapter 2
The simpler idea of using a single loop of wire around the end of the sensor barrel was more
useful. The circuit was connected directly to a 20 MHz analogue oscilloscope to obtain a
smooth trace (amplitude noise less than the thickness of the trace) with a period of 10- 6 s,
which is in agreement with the manufacturer's stated operating frequency of 1 MHz. The EMF
across the loop had a sinusoidal form that varied with time, t, as
V = V0 sin (2Jift) (2.3)
where V 0 is the amplitude and f is the frequency. Faraday's law gives the relation to the
magnetic flux, r/Jm, through the loop as
with
V= -dr/Jm dt
r/Jm =BA
(2.4)
(2.5)
where B is magnetic flux density and A is the area of the loop. This leads to an expression for B
B = - ~ f V (t )dt
=-~ fsin(2Jift )dt
V: = --0 - cos(2JTft) +constant A271/
(2.6)
When the EMF is at a maximum or minimum, the field is changing at its fastest rate
(corresponding to B = 0), so there is no offset and the integration constant is zero, thus
B = B0 cos(2Jift) (2.7)
with the amplitude of the field
B=~ 0 A271/
(2.8)
With no target present the EMF across the loop was measured as 0.134 V, so using the barrel
diameter of 73.7 mm gives an estimate for the field amplitude B0 - 5 x 10- 6 T.
The coil can be modelled as a solenoid such that the flux inside the coil is constant except
near the edges where its magnitude decreases as the field lines diverge. The test loop was fitted
near the end of the sensor barrel and so an estimate of the magnitude of the current in the coil, /0,
can be estimated by the simple function
31
Chapter 2
(2.9)
where f.J.o is the permeability of free space and n is the number of turns in the coil per unit length
of the coil; this assumes a one-layer thick coil. Using the estimate of B0 gives the estimate
n/0 - 10 A.turns.m -J. If the coil has, say, 1000 turns and is approximately 8 cm long, then the
current in the coil, /0 - 10- 3 A, which is a reasonable value that gives confidence in the
suitability of the B0 estimate.
2.3 MagnetoaResistive Sensor
The equation describing the rotation of the magnetisation with applied field (2.2) shows that the
magnetoresistive (MR) effect is non-linear. The effect can be linearised by depositing
aluminium stripes - so called Barber poles - on top of the permalloy at 45 a to the strip axis.
The conductivity of aluminium is larger than the permalloy and so the strips rotate the current
direction through 45 a. The current follows a zigzagged pattern which effectively changes the
angle of rotation of the magnetisation relative to the current from a to a- 45 a. For the Philips
KMZ series of MR sensors four permalloy strips are arranged as the arms of a Wheatstone
bridge arrangement. For two diagonally opposed strips the Barber poles are at + 45 a and - 45 a
to the strip axis. When an external magnetic field is applied, as the resistance increases in one
pair of strips it is matched by a decrease in resistance in the other pair. The result is a bridge
imbalance that is linearly related to the magnitude of the applied magnetic field.
Philips state that their KMZ10A thin-film permalloy MR sensor is suitable for a wide range
of applications including navigation, current and field measurement, revolution counters,
angular and linear position measurement and proximity detectors [33]. The navigation using
Earth's magnetic field (- 5 x 10- 5 T) was of interest because the estimate of B0 given in the
previous section ( § 2.2) is just an order of magnitude less (- 5 x 10- 6 T). It was anticipated that
with suitable amplification circuitry these devices could be used to measure the field. The
KMZ10A devices were selected because of their availability and the fact that they are quoted as
being capable of operating at 1 MHz.
2.3.1 Amplification Circuit
As a quick trial the MR device was tested by connecting it directly to a power supply and an
oscilloscope. This demonstrated that the device was functioning normally and a reading was
obtained when a magnetised screwdriver was placed in its vicinity. However to detect weaker
fields an amplification circuit must be used; the Philips data sheet [33] gives a basic application
circuit which was constructed on a PCB. The circuit allows for sensor offset and sensitivity
32
Chapter 2
adjustment, as shown by the circuit diagram of figure 2.3. Temperature drift is an important
consideration and the circuit diagram shows the use of a compensatory silicon device with a
positive temperature coefficient (R6). However, this device cou ld not be sourced, so by plotting
the expected resistance response to temperature a suitable resistor was found to optimise the
circuit for the laboratory temperature.
r-~--~----------~----------~r---~------------~~~:5V sensitivity offset
adjustment R7 R1 R2 R5 2.4 kll
500 kll 140 kll
RB 2.4 kl.l
R9 33 kll
R11 22kll
R10 33kll
adjustment
,li>--7 +---oVa: 0.2 V to 4.8 V
Ct 10 nF
(with resistive load greaterthan 10 kll)
MBH687
Figure 2.3. Amplification circuit used with the MR sensors. Adapted from [33].
The PCB was double sided and space between tracks was left un-etched and grounded to
reduce noise levels and the resulting circuit is shown in the figure 2.4.
Figure 2.4. Constructed amplification circuit with the MR sensor protruding from the left-hand edge.
33
Chapter 2
2.3.2 Circuit Testing
The circuit was tested by connecting the output to an oscilloscope and moving a magnetic field
from a screwdriver in the vicinity of the MR sensor. The result was a response at a higher
amplitude voltage level than was obtained with the circuit in the previous section (§ 2.3.1), as
would be expected. However, when the MR sensor was placed near the IDS coil, no response
was noticeable above the background noise levels. There were two possible reasons for this,
firstly the circuit may not have been sensitive enough and secondly the frequency of the IDS
coil may have been too high for the sensor to detect.
To investigate the frequency response of the MR sensor, the IDS coil was removed from the
usual oscillator/demodulator circuit and connected to a frequency generator. The lDS coil was
placed above the MR sensor, but no response was found at any frequency. At 1.00 MHz the
coil voltage was 427 m V and the influence on the field sensor as monitored on the oscilloscope
was a low-level background noise(- 1.0 MHz, - 1.26 mV). At 400kHz the coil voltage was
182 mV and there was no distinguishable effect over the background noise (- 3.4 MHz,
- 2.5 mV). The lower coil voltage is a result of a shift down from the resonance frequency of
the coil. Similar experiments using a different coil with a much lower resonance frequency of
35 kHz also failed to yield a useful signal response. It is suspected that the low voltage and
current provided by the signal generator produced a field of insufficient intensity for the MR
sensor to detect. The KMZIOA data sheet shows that the response to magnetic field decreases
as the frequency increases, so the lack of response from the circuit was likely to be a result of
the combination of low amplitude and high frequency. Hence this device was shown not to be
appropriate for this application.
2.4 Test Coil Sensor
Besides the MR sensor, the other magnetic field sensor identified in § 2.1 that fulfils the
requirements of § 2.2 is the test coil. Equations (2.3) to (2.8) can be used to determine the
amplitude Bo given a measured potential difference (V0) across the test coil. However, since the
coil consists of multiple loops, the total flux is that passing through an individual loop
multiplied by the number of turns in the coil, N. Therefore the magnetic flux density can be
determined from the measured EMF by
B = Vo o AN2Jlf
(2.10)
A simple test coil was formed by wrapping 26 gauge (0.4038 mm) enamelled copper wire in
28 turns around a plastic former of diameter 11 mm and length 10 mm. A glass capillary tube
34
Chapter 2
was used as a holding support for the tube and the signal wire passed though the middle and out
the end to an oscilloscope. The coil is conducting, but it does not interfere with the operation of
the lDS since it is stranded and therefore eddy currents cannot be generated in it. However, it is
not possible to measure a physical quantity from a system without affecting the system itself. In
this situation, the coil takes energy from the field and will have some influence on the system.
copper wire
Signal wire out ~
Non-conducting holding rod
Figure 2.5. Simple test coil construction.
Placing the test coil below the lDS coil produces a clear sinusoidal signal with a I MHz
frequency. Immediately below the sensor coil the magnitude of the potential difference across
the test coil was recorded at 84 m V; corresponding to B0 = 5.0 x 10- 6 T. The values given by
the test coil are in agreement with the estimates in § 2.2.
2.5 Selection and Refinement of Test Coil
It can clearly be seen that the results from the test coil are much more stable and well defined
than from the MR sensor. Test coils are well suited to measure the AC magnetic fields
generated by the lDS coil since Faraday's law relies on changing fields to generate a potential
difference. This effectively eliminates the static background effect of Earth's magnetic field.
The test coil was used to measure the magnetic flux density profile of the lDS coil, as shown
in figure 2.6. The test coil was positioned immediately below the lDS coil and the vertical
component of the flux recorded at different displacements from the centre position. It can be
seen from this profile that, as expected, the field is strongest in the centre and decreases
outwards. At the edges of the lDS coil, the field drops by an order of magnitude and at a
displacement of 35 mm from the centre - which corresponds to the edge of the IDS coil - the
field is 36 % of the centre value. Beyond 35 mm the flux density was very small and with the
trial test coil the signal was lost in the background noise. Consequently careful design of the
test coil was required to give strong coupling to the lDS coil.
35
5
r-~ 4
I 0
2
-40
Chapter 2
-20 0 20 40
x /mm
Figure 2.6. Magnetic flux density profile of the lDS coil as measured with the test coil.
2.5.1 Test Coil Construction
The test coil described in § 2.4 was refined to give a stronger signal towards the edge of the lDS
coil. The use of a core with a high permeability would increase the potential difference across
the test coil but this would interfere with the operation of the lDS since eddy currents can be
generated in the material. Another way to increase the signal is to increase the total area of the
coil by increasing the number of turns or the diameter of the core. A good coil has a large
number of evenly-spaced, tightly-wound loops.
The test coil design process went through many stages before a final refined option was
developed. Test coil 'a' shown in figure 2.7 was constructed using 32 gauge (0.2032 mm)
enamelled copper wire with an air core and was held together with wire braces. It was found
that the wire braces produced spikes on the signal and so coil 'b' was constructed in a similar
way, but was held together with masking tape. For both of these designs the intention was for a
flat sensor, so that only the vertical component of the field was detected. Their actual height
was - 2 mm, which limited the number of turns to - 40 and so a strong signal could not be
obtained. More turns were introduced in test coils 'c' and 'd' which had lengths of- 6 mm and
were constructed on paper formers. These test coils had approximately 80 turns and produced
clear signals with improved amplitude. Coil 'e' demonstrated the use of finer 40 gauge (0.0787
mm) wire enabling a higher turn density.
36
Chapter 2
I l
1 '
I
(b) liHfl(lllffilllllll cc) ~ IIII)Uilllllljllll]ll (d) Jllllill~illllffi (e) am1mnm 1 tfo th 112 I 1 3 14 titS ita ili ' 1!8 ili
Figure 2.7. Different coil designs.
During the development of test coils 'a'-'d' marked improvements in signal to noise ratios
and sensitivity were recorded, however these coils were flimsy and were not suitable for making
a large number of measurements. The final test coi l 'e' in figure 2.7 was a much improved
design that uti lised a non-conducting solid core and two end pieces to hold the wire in place; the
construction is shown in figure 2.8. The test coil had 200 turns which gave a voltage of 240 m V
at the centre of the IDS coil.
, .. 11 mm "I
}mm , ..
9mm
"' (a) (b)
Figure 2.8. Optimised test coil design. (a) Side view. (b) Projection view.
2.5.2 Test Coil Characterisation
The impedance of the test coil was measured using an Agilent 40Hz - 110 MHz impedance
analyser. This device sweeps through a range of frequencies to determine impedance as a
function of frequency , as shown in figure 2.9. The peak in impedance magnitude of 113 ill is
at 1.38 MHz, which also corresponds to the point where the impedance phase changes from
+ 90 o to- 90 °. Note that this is a peak in the complex magnitude of the impedance and does
not correspond to a re istive peak.
37
"' "' ~ 00
" "0 -Q::,
Chapter 2
100 150 ·-·----··--·-·-·-··------······----··--·
50 c: 100
0 -"
~ 50 -50
- lOO
0.1 10 0.1 10
f I Hz f I MHz
(a) (b)
Figure 2.9. Impedance analysis of the test coil. (a) Impedance phase angle 0. (b) Impedance magnitude IZI.
The form of figure 2.9 indicates that the coil is a parallel R, L and C circuit as shown in figure
2.10 and the peak corresponds to parallel R, L and C resonance. The resistance, R, results from
the length of wire, the coi l loops result in an impedance, L, and the capacitance, C, is the
consequence of charge building between loops. The impedance of the coil, Z, can be regarded
as the opposition to current flow, I , such that the potential difference across the inductor is
V= I Z . The inductive element of the coil impedance is X L= iwL , where i = ~, w is the
angular frequency of I and L is the inductance. The capacitive element of the impedance is
X c = 1/iuC , where C is the capacitance. The admittance, Y, is defined as the reciprocal of
impedance, i.e. Y = 1/Z, and for the parallel LR and C circuit is given by
1 Y= +iwC
R + iwL (2 .11 )
In polar form, Y = IYicp, this is
(2.12)
At resonance the phase angle, cp, is zero and equation (2. 12) shows that thi s is when
(2.13)
38
Chapter 2
and thus the resonant frequency is
(2.14)
At resonance when the phase angle is zero, the impedance is entirely real and thus from
equation (2.11) and using equation (2.13)
Y= R = R R 2 + mr/ L2 L/C
Z=~ (2.15)
RC
The AC resistance is much higher than the DC resistance because of the skin and proximity
effects. Passing a direct current through the test coil reveals that R = 13.3 n. Substituting this
value and the resonance data from figure 2.9 into equation (2.15) gives a values of
L = ~ ~ZR- R 2 = 8.8 X 10- 4 Hand c =L/ RZ = 5.9 X w-IO F.
c
Figure 2.10. Parallel R, L and C circuit model of test coil.
2.6 Collection of Data
With the test coil designs completed, it was then appropriate to test the collection of data. Initial
tests revealed low level noisy signals and efforts were made to improve them using a phase
locking technique.
2.6.1 Signal Noise
The test coils were connected to an Agilent 500 MHz 2 GSa.s- 1 digital oscilloscope and the
traces were recorded. The recorded signals were found to be subject to noise and fluctuations
39
Chapter 2
that made them difficult to use. Figure 2. 11 (a) demonstrates the fluctuations over 200 cycles
with a sample rate of 100 MSa.s - 1 and it is clear that there is not a smooth signal as the
amplitudes vary from 2.5x 10 - 3 -7.5x 10 - 3 V. Figure 2.11 (b) shows high frequency noise on
the signal over 10 cycles.
l.E-02
5.E-03 5.E-03 > -g O.E+OO -;;; O.E+OO " bJl en
-S.E-03
- l .E-02 -+-----.-----,---,.------j
O.OE+OO 5.0E-05 l.OE-04 1.5E-04 2.0E-04
t I s
(a)
bJl
en -S.E-03
- l .E-02 -+----.---.---,.-----.-~------"
O.E+OO 2.E-06 4.E-06 6.E-06 8.E-06 l.E-05 I Is
(b)
Figure 2.11. Signal recorded from a test coil. (a) Global varia tions. (b) Local variations.
To clean up the signal, the digital oscilloscope includes an averaging fac ility that takes the
mean of repeating functions. However this was not used because it was expected that in
practical use, the amplitude of the field would vary over time and this information would be lost
in the average. So a phase- locki ng technique was employed, which relies on knowing the basic
form of the signal that is being measured. The noisy time-dependant input signal g (t) is
compared to a known smooth time-dependant reference signal f(t) by means of a general
correlation funct ion
R(o)= Lim- J(t) g(t+o)dt 1 {r t ->~ T
(2.16)
which relates f and g for a time parameter c5 and where T is just the upper integration li mi t. R is
zero when f (t) and g (t) are independent. Generall y g (t) is modulated in some way by the
referencef(t) . In the case of the IDS the signals are known to be periodic sine functions with
ampl itudes a , and a2 and of frequency cv, thus the correlation function becomes
a a f, "T R(nT, r/J ) = - 1-
2 sin(wt )sin(UJt + rp )dt nT o
a a =-1 -
2 cos rp 2
(2.17)
40
Chapter 2
which has an upper integration limit of nT where T is the period of the frequency w and n is an
integer. rp is the phase difference betweenf(t) and g (t). For complete correlation R is taken as
unity and if the amplitude of f(t) and the phase difference are known, the amplitude of the
signal may be determined. This technique is appropriate to the test coil signal because the
signals are small, periodic and noisy.
Lock-in amplifiers apply phase-locking and can be used to reduce the noise on a signal where
there is a clear reference. A lock-in amplifier was tested and a smooth reference signal was
taken from several loops of wire wrapped round the IDS barrel. However it was found that this
instrument was not suitable for the high frequency signal from the IDS and on further
investigation revealed that I MHz devices are uncommon.
2.6.2 Phase-Locking Program
Given the inability of the hardware lock-in amplifier to resolve the signal, an offline software
solution was investigated. The digital oscilloscope was able to record actual values from the
signal which enabled the development of a Java application to phase-lock the recorded signal.
The signals were stored as text in comma separated value (CSV) formatted files. The program
extracted data from a specified file and proceeded to multiply the signal and reference together.
The product was then integrated and the resulting amplitudes plotted on the graphical user
interface (GUD. The phase difference between the signal and reference was adjusted by moving
a sliding bar and both an average amplitude and amplitude variance were calculated. Figure
2.12 shows a screenshot from the program. An optimisation method was developed to find the
phase that gave the minimum amplitude variance i.e. the smoothest output signal. The resulting
amplitudes array could then be saved to a file in CSV format to enable display in a graphing or
statistical package.
41
Chapter 2
.. . l:...li;ll.l!1
~ -- ~-- =~ ~· ...... p; ... ... __
{:0 t•t4038108736C893
' ,_. --- .~ 1 I '~ I Pl12 PI 4AI3 -
Figure 2.12. Screen-shot from the phase-lock Java application.
Figure 2.13 shows the result of phase-locking a noise signal with the program. Although it
may appear irregular, it is smoother than the unprocessed signal. The average amplitude is of
the unprocessed signal is 4.65 x 10 - 4 V with a variance of 4.39 x 10 - 7 V2. The phase-locked
signal has a mean amplitude of 0.0324 V with a variance of 1.12 x 10 -? V2•
> .._ .g 0.033 .@ 0.. ~ ~ 0.032
iZi
0.031 +-----------,,-----,-------1
O.OE+OO S.OE-05 l.OE-04
t I s
l.SE-04 2.0E-04
Figure 2.13. Result of phase-locking an input signal.
For practical purposes a second application was developed without the GUI to process the
recorded signals in bulk. A list of input signal and reference fi les were given to the program
that then opened the fi les, found the optimum phase difference and saved the resulting
42
Chapter 2
amplitudes to an appropriate CSV file. With this program a set of readings from a whole
experiment could be processed in one batch.
2.7 Summary
This chapter has described a number of magnetic field sensing technologies and has discussed
their relative merits and suitability for measuring the field around an lDS coil. An initial
investigation showed that the field oscillated in a sinusoidal manner with an amplitude of
- 5 x 10- 6 T and a frequency of I MHz. Magneto-resistive sensors and test coils were selected
as being the most suitable devices to measure fields of this form. Initial investigations of a
Phi lips KMZIOA M-R sensor were unsuccessful and this was attributed to a combination of the
high frequency and low strength of the field. Trials of a test coil device were more fruitful and,
after a number of refinements, a suitable coil was constructed. The signal from the test coil was
found to be very clean at high field strengths, but for low field strengths ( < 2 x 10- 6 T) the low
signal to noise ratio was found to be a serious issue. To address this problem, the signal was
recorded with a digital oscilloscope and then a phase-locking program was built to extract the
amplitudes from the noisy pattern. Before processing, an example signal was found to have a
mean amplitude of 4.65 x 10- 4 V with a variance of 4.36 x 10- 7 V2, but the phase-locking
technique revealed an amplitude of0.0324 V with a variance of 1.12 x 10- 7 V2• The result was
a reliable system that could be used to measure the magnetic field around IDSs.
43
Chapter 3
Finite Element Analysis
In the first chapter it was hypothesised that small magnetic field changes that are not detected by
coil impedance measurements can provide more information about the target material. The
previous chapter described the development of a sensor that was suitable for measuring the
small fields around IDS coils. This chapter leads on from this by describing how finite element
analysis (FEA) was used to determine what field features can offer useful additional information.
Firstly there is a description of the electromagnetic finite element modelling processes and how
it was applied to the IDS coil and target arrangement. Both two- and three-dimensional models
were constructed using a commercial software package and there is a discussion of the relative
merits and applications of each. The models provided a large number of data, so a convolution
program was developed to take the magnetic field solutions and extract measurements of a
similar form to those taken by the test coil experiments.
3.1 Generalised FEA Modelling Process
Analytical solutions to eddy current problems are described by Dodd and Deeds [34] who give a
quick and easy method for the calculation of observed effects. However, the solutions presented
there are not appropriate for high frequencies. This is because as the frequency of current in a
wire increases, the current density ceases to be uniformly distributed and tends to concentrate at
the surface, which causes the coil resistance to increase and the inductance to decrease. This
leads to an effect where the current tends to flow across the turns rather than through them and
the capacitance between the coil and target increases. So given that an analytical solution is not
available, numerical approximations are needed.
In general terms the finite element method is used for the solution of physical problems that
are described by differential equations. The continuous domains of the problem are broken
down into a finite number of elements. Chari and Silvester [35] and Silvester and Ferrari [36]
describe the finite element method with particular reference to electrical and magnetic field
problems.
There are a number of commercially available software suites that enable FEA of
electromagnetic problems. Simulations for this thesis have used Ansoft's Maxwell software
44
Chapter 3
suite, which consisted of two main programs that could be used to solve problems in two- or
three-dimensions. The programs used FEA to numerically solve Maxwell's equations over a
specified geometry and within user-defined boundary conditions. All simulations were
completed on the same 2.2 GHz, 5 I 2MB RAM PC with the Microsoft Windows XP (service
pack one) operating system. Therefore it was possible to use the time taken to complete the
FEA to compare the efficiency of various methods.
3.1.1 Setting Up the Simulation
The first stage of the modelling process is to construct the problem geometry to give the
program the physical constraints within which the solution is to be found. Then the material
properties such as the relative permeability, J1, relative permittivity, £, and conductivity, a, are
entered; this may be done manually or common materials can be selected from a predefined
catalogue. Following from that, sources and boundary conditions are entered, which define the
problem to be solved. One or more of several so-called executive parameters may be selected,
which are quantities such as force, torque, inductance, capacitance, or power loss. These
parameters may arise as a result of fields generated by the sources and can be determined by the
program. The program will then proceed to solve the problem through using a FEA method by
generating a mesh and calculating the field solutions. Results can be extracted through the use
of a post processor program that uses the field solutions to determine various properties such as
magnetic field strength.
3.1.2 Impedance Simulation
The Maxwell software allows for the calculation of an impedance matrix, which summarises the
relationship between AC voltages and currents in multi-conductor systems. For a two
conductor system, the equivalent circuit is shown in figure 3.1, which is a generalised form of
that given in figure 1.3.
45
Loop 1 (IDS coil)
Loop 2 (target)
Figure 3.1. Equivalent circuit for a two-conductor system.
The potential difference across each loop are given by
This leads to the matrix expression
Chapter 3
(3.1)
(3.2)
(3.3)
where Z1 = R1 + iwL1 is the impedance of loop one, Z2 = R2- iwL2 is the impedance of loop two
and ZM = RM + iwLM is the mutual impedance between loops one and two. For a system with 11
conductors, the impedance matrix contains 11 x n elements. Once the field solver has completed,
the impedance solver can use the field values to calculate the inductance and resistance values
separately before combing them into the impedance matrix.
The inductance is calculated from the average energy of the system, U , which is given by the
integral of the magnetic field density, f1, and magnetic field, H, over the volume, V, of the
problem, thus
U =.!_ fB·H* dV 4--v
At any point in the current cycle, the energy of the system, U, is given by
(3.4)
(3.5)
where L is the inductance and I is the current at a given in time. Integrating over the current
cycle, gives a second expression for U
46
Chapter 3
(3.6)
where IRMS is the root-mean-square current and fpeak is the peak of the current cycle. Thus the
inductance can be determined from
lll·H*dv L=----:::-
I~eak (3.7)
The Maxwell program takes /peak = 1 A. turn- 1 and so a value for the inductance can be
calculated.
The resistance is calculated from the power that it dissipates, which is given by the integral of
the current density,!._, over the volume of the problem, thus
P = -1- fl · J* dV 2 --av
A second expression for the power is
2 1 2 p = R / RMS = l R J peak
Thus the resistance can be determined from
Coil Impedance Estimate
~ lLL*dv R=--,--
I~eak
(3.8)
(3.9)
(3.10)
To compare the result of the simulations with the actual coil values, an estimate of the coil
impedance was found using some of the estimates from section § 2.2. The resistance of the coil
can be estimated by treating the coil as a hollow copper cylinder with a thickness of 1 mm, a
height of 75 mm and a diameter of 70 mm. This gives a value of R- 5 x 10- 5 n. The
inductance can be estimated by treating the coil as a solenoid with an air core such that
(3 .11)
where N is the number of turns in the coil, A is the coil area and l is the coil length. This yields
a value of L - 10- 3 H for a 1 00-turn coil and L - 10 -? H for a single-turn coil.
47
Chapter 3
3.1.3 Eddy Current Solver
The eddy current field solver is used to simulate the influence of time-varying magnetic fields
on conductors. All time-varying fields, £(t), are assumed to be sinusoidal and oscillating at the
same frequency, w, and phase, B, with the form
(3.12)
where F0 is the field amplitude. All fields must have the same frequency, but do not have to be
in phase. Problems involving non-sinusoidal fields must be broken into harmonics and solved
at each frequency. For the IDS coil and target system the magnetic field measurements
described in section § 2.2 show that the field is of the form of equation (eq 3.12).
Maxwell's equations for the fields in the problem are
oB VxE=---= - of
V-B=O
oE Vxfl=fLl+fLE
0--;
(3.13)
(3.14)
(3.15)
(3.16)
where §;_ is the electric field, !1 is the magnetic flux intensity, p is the charge density, E: is the
permittivity, f1 is the permeability and .f. is the current density. There are also a number of
relations: magnetic flux intensity and magnetic field, !1 = JlH; electric flux and electric field,
D = cf;.; and current density and electric field, .f.= crf;_, where fJ is the conductivity. Fields in the
form of equation (3 .12) can be expressed as
and therefore
and
F(f) = Re[F0 exp(iB)exp(imt )]
ofl. =iwB of
of;_ =iwE or
Thus Maxwell's equations (3.14) and (3.16) for a time harmonic field can be expressed as
(3.17)
(3.18)
(3.19)
48
Chapter 3
VxE=-iwB - - (3.20)
V x.lB = aE + iwEE Jl- - -
(3.21)
Let a vector potential, A, be defined with the equation
B=VxA - - (3.22)
Equation (3.22) may be substituted into equation (3.21) to give
V x-}(V xA) = afi + iwcfi (3.1)
As described by Weiss and Csendes [37] a solution for !1.. in terms of A and qJ is given by
!1.. = -iwA- V rp (3.23)
where qJ is a scalar potential function. Substituting this into (3.22) yields
(3.24)
The right-hand side of this equation is of the form of a complex current density with the three
components. The electric potential results in a source current density
Js =-aVrp (3.25)
Time-varying magnetic fields result in an eddy current density
(3.26)
The remainder is the result of time-varying electric fields and can be described as a
displacement current density
(3.27)
The sum of equations (3.25), (3.26) and (3.27) is the total current density, Jr. When modelling
conductors connected to an external source, the total current in the conductor, fr, must be
specified and thus lr is specified by the integral over the cross-section of the conductor Q
(3.28)
The eddy current solver calculates eddy currents by solving for A and qJ in equation (3.24) and
utilising equation (3.28).
The eddy current solver cannot use these equations for non-linear materials because although
the current is sinusoidal, the fields associated with non-linear materials consist of a number of
49
Chapter 3
harmonics. Ansoft's Maxwell programs utilise an effective magnetic flux density and effective
magnetic field intensity, which depend on the frequency of the harmonics. This is described in
more detail in the Ansoft technical manual [38].
3.ll.4 Solution Criteria and Meshing
The FEA solver breaks the problem space into a mesh of smaller elements over which the
program can solve the differential equations. In general, the elements may be any shape, but in
the Maxwell program triangles and tetrahedrons are used for two- and three-dimensional
problems respectively. A number of options are available to produce a solution with the desired
accuracy. The meshing process can be wholly automatic, wholly manual, or a combination of
both.
The entirely automatic process generates an initial coarse mesh that is refined over a number
of passes. After each pass, a value of the error in the field is calculated and the mesh is refined
by a specified amount to reduce this error for the next pass. Once a user-specified target error
has been reached, the solution process will stop. To put an upper limit on the maximum time
that the solver will attempt to meet this target, the user may also specify the maximum number
of passes that are to be completed before the process will stop regardless of the error. The result
is a finer mesh around material boundaries and in the corners of objects.
The manual meshing process allows the user define smaller elements in specific areas of
interest; that particular mesh is then solved on an as-is basis. The final meshing method
involves a combination of both manual and automatic processes; the meshing program is given
a direction with a manual initial mesh and then the automatic refinement process is applied.
The solution process for finer meshes is more computationally intensive and requires more
memory than coarser meshes. So the desired accuracy must take account of the available
resources. For example, with the IDS and target arrangement, the area between the coil and the
target is of particular interest and so the space in this region can be refined while the remainder
of the problem can be left with a relatively coarse mesh. The result is that the error in the field
between the coil and the target is lower than other areas that are not of particular interest.
The meshing process can be controlled by specifying mesh properties for individual objects,
which can be done by either setting the maximum element size or the maximum number of
elements. This can be exploited by using dummy objects that have no electrical properties, and
no function in the problem, but have tighter mesh properties than the surrounding areas. For
example, the region between the IDS coil and target can include a dummy object with a much
finer mesh than the surrounding region and so more accurate field solutions will be found in that
particular area of interest.
50
Chapter 3
Within each solver pass there is also an iterative process to refine the field solution; the
maximum number of iterations can be specified before the solver is started. A normalised error
quantity called the solver residual is used to specify acceptable tolerances for the solution; for
linear materials there is a linear residual and for non-linear materials there is a non-linear
residual. A residual is calculated after each iteration: if it is higher than the specified value a
correction is added and another iteration is completed, if it is lower than the specified value then
no further iterations are run.
The Maxwell program can produce solutions through one of two methods. The first is a
direct method that will always converge to a solution and the second is a more intelligent
method that is generally faster for problems with large meshes, but does not always converge.
The decision as to which method is used can be left to the program by selecting the automatic
mode that makes an estimate of whether the faster method will work. If the estimate is incorrect
and the faster method does not appear to be converging, then the process is stopped and the
direct method is used.
3.2 TwoaDimeJrnsJional IFEA
Ansoft's Maxwell 2D Field Simulator uses FEA to numerically solve two-dimensional
electromagnetic problems. A problem is entered into the program and field solutions are
calculated as described above. Two-dimensional simulations are appropriate to schemes such as
the IDS coil with a target centrally positioned below it.
3.2.1 Test Problem
A basic model of the IDS sensor coil and target arrangement was used to investigate the
effectiveness of the two-dimensional FEA.
Geometry
One of two coordinate systems may be utilised for drawing the geometry of a two-dimensional
problem. The first is an xy-plane Cartesian coordinate system, which is appropriate for any
cross-sectional geometry. In this system, the current flows in the z-direction and therefore the
magnetic field lies entirely in the .xy-plane with no z-component. The second is an rz-plane
cylindrical coordinate system, which is suitable for axial-symmetric problems. In this system,
current flows in the 8-direction around the device's axis of rotational symmetry and therefore
the flux only has components in the rz-plane. The problem geometry of the IDS sensor coil
with a centred target can utilise the latter scheme, as shown in figure 3.2. It should be noted that
using this coordinate scheme means that the target is modelled as disc rather than a rectangle.
51
Chapter 3
The assumptions about the geometry of the coil were taken from a discussion with the UK
supplier of the IDS and from the Kaman user manual [ 1 0]. The coil is taken as being a 1 mm
thick cylinder with an external diameter 1 mm less than the outer carbon fibre protective casing.
The target was taken as being a 5 mm thick rectangular plate positioned at d, = 10 mm, with a
width 3 times the coil diameter to avoid problems associated with small targets (§ 1.4.2).
lDS coil cross
section
' Vl I '< I 3 : 3 1(1) 1:::;' I '<
35
~ I 79
/
Target
d,
:~O!!l~~~~~~~~·:fs I )08 I I I
r
Figure 3.2. The axial-symmetric geometry of the lDS sensor coil and centred target. Dimensions given in mm.
Materials The IDS coil was assumed to be a copper construction and therefore appropriate material
parameters were selected: t:,. = 1.0000000, p,. = 0.9999910, a= 5.8000000 x 10- 7 S.m- 1. For
the purposes of the simulation the target was taken to be aluminium with t:,. = 1.000000,
p,. = 1.0000210, a= 3.800000 x 10- 7 S.m -I. The remainder of the problem space was set to be
a vacuum (c,. = 1.0000000, Jlr = 1.0000000, a= 0.0000000 S.m- \ which is a good
approximation to air (c,. = 1.0006000, p,. = 1.0000004, a= 0.0000000 S.m- 1) and was expected
to result in a faster solution.
Boundaries The IDS coil consisted of wound copper wire and so eddy currents could not develop in it,
therefore in the simulation it was set to be "stranded". The aluminium target, however, did
experience eddy currents on the surface as a result of the excitation from the coil, therefore the
default Neumann eddy current boundary was applied. Using the estimate of the coil current in
section § 2.2, the current density in the coil was estimated to have a magnitude, 10 = 10 4 A. m- 2
52
Chapter 3
over the whole cross-section. The outer balloon boundary that contains the whole problem was
set to pad all the problem geometry by 200 %.
Solution
The impedance matrix was set to involve the coil and the target material. The solution criteria
were set so that the solver used the automatic mesh process with 15 % refinement per pass to
solve for both the field and the impedance matrix with a residual of 10 - 5. The solver was then
set to find a solution with a maximum error of 1 %, which took approximately 30 seconds on
the computer specified in section § 3.1.
Results The impedance matrix yielded a coil resistance of 1.617 x 10- 4 n and an inductance of
4.051 x 10 - 8 H. The inductance value is the result for a single-turn coi l and so there is
agreement to within an order of magnitude with the estimate of coi l impedance found in section
§ 3.1.2.
A plot of the magnetic field calculated by the simulation is shown in figure 3.3. This shows
that the FEA has produced field results that instinctively make sense in terms of a simple
representation of the problem i.e. the field is strongest around the coil and decays with
increasing distance from it and the field is compressed by the target and the eddy currents
generated in it. The edge of the target affects the field such that it appears to bulge at this point,
which is discussed in section § 3.4.2.
lDS coil cross-section
Target
> I0 - 5 T
I0 -6 T
I0 - 7T
< IO - s T
Figure 3.3. The magnetic flux plotted for the two-dimensional test problem. The central lighter portions represent a stronger field than the surrounding darker regions.
53
Chapter 3
A plot of the magnitude of the z-component of the field taken along a line parallel to the
target, but 1 mm below the base of the lDS coil, is given in figure 3.4. On this plot radius
R = 0 mm is the left-hand edge of the problem space, which is the centre of symmetry and lies
below the centre of the lDS coil. It is the magnitude of the z-component that is of interest, since
this is the quantity that is measured by the test coil system described in section § 2.5.2. The plot
reveals local discontinuities which result from areas of the mesh that were not well refined.
Recall that the external radius of the simulated lDS coil was 36 mm and this corresponds to the
point on the figure where the plot drops to zero. This zero figure means that the field no longer
has a z-component and - recalling that the field cannot have a B-component - must therefore
only have an R-component. Investigation of the phase revealed that the field flips direction at
this point, which instinctively makes sense in terms of a simple representation of what is
happening to the field from the coil: at a given point in the coil's current cycle the field lines
extend downwards from the centre of the coil (strong vertical component); below the edge of
the coil the field lines are horizontal (weak vertical component); and outside the edge of the coil
the field lines loop upwards to the top of the coil (strong vertical component).
4
3 f-
"' I 0 2
et)'
0 50 100 Rlmm
150 200
Figure 3.4. Variation in the magnitude of the z-component of the field, !Bzl/ tesla, with radius, R I mm, along a line 1 mm below the lDS coil.
The form of figure 3.4 is in agreement with the field measurements shown in figure 2.6 and
the magnitude of the field below the central portion of the lDS coil also agrees approximately
with the measured value of- Sx 10- 6 T.
3.2.2 Simulation Refinement
The test problem simulation produced good results that appeared to reliably represent the form
of the experimentally measured field. The error for the test problem was set at 1 % but the
54
Chapter 3
discontinuities found in figure 3.4 demonstrated that this value did not correspond to the actual
error in the field solution. The meshing process required more refinement to produce a more
accurate field solution and smoother plots that could reveal more detailed information.
Therefore a dummy object ( § 3 .1.4) was introduced to decrease the mesh size in the region of
interest i.e. the space between the coil and the target.
35
IDScoil ~ cross- ~ ----._
section : 79
Dummy meshing object
Target
r
Figure 3.5. Axial-symmetric geometry of the IDS sensor coil and centred target with the inclusion of a dummy object to improve meshing. Dimensions given in mm.
Figure 3.5 shows the addition of the dummy object to the test problem geometry. The object
is simply a vacuum region within which the mesh is set to have a low initial element size. The
maximum element area in the dummy object was set to 0.5 mm2• Figure 3.6 compares the mesh
without (3.6(a)) and with (3.6(b)) the dummy object. It can clearly be seen that there are more
elements in the area of interest in the mesh with the dummy object.
55
Chapter 3
(a) (b)
Figure 3.6. Mesh in the space between the coil and target. (a) The original problem without a dummy object. (b) The problem with a refined mesh inside the dummy object.
The fi eld solution took about the same time as the original problem (- 30 s) and the results
are demonstrated by the plot in figure 3.7. Comparing this graph with figure 3.4 shows that the
addition of the dummy object has successfully improved the continuity of the solution in the
region between the IDS coil and the target, without a noticeable increase in the solver time.
4
3 f-
"' I 0 2
cci' I -
0 0 50 100 !50 200
Rlmm
Figure 3. 7. Magnitude of the z-component of the field , IB,I I testa, with radius, R I mm, along a line 1 mm below the IDS coil, for a geometry with a meshing dummy object.
3.2.3 Parametric Test Problem
Using the basic model of the test coil and target, a parametric prob lem was constructed to
demonstrate the influence of different target displacements on the field . This was achieved by
setting a constraint, dr. from the base of the coil to the top of the target that was swept in five
56
Chapter 3
steps over the range d1 = 0, 5, ... , 25 mm. The whole solution took approximately 2.5 min,
which is what would be expected given that one solution took 30 s.
The impedance matrix was calculated for each step and the variation of inductance with d1 is
given in figure 3.8. As d1 increases, the mutual inductance, M, between the coil and target
decreases as the coupling between the two systems decreases. Equation (1.8) shows that a
decrease in M corresponds to a decrease in the coil's equivalent resistance. Conversely,
equation ( 1.9) shows that the decrease in M leads to an increase in coil's equivalent inductance.
This theoretical analysis is mirrored by the simulation results. A further simulation, with
d, = 50 mm, showed that the curve tended to 4.36x 10- 8 H as the target's influence decreased.
";' 4.2 0
X
::t
-.J 4
5 10 15 20 25
Figure 3.8. The variation of coil inductance, L, with target displacement, d1•
3.3 Three~Dimensional FEA
Ansoft's Maxwell 3D Field Simulator uses PEA to numerically solve three-dimensional
electromagnetic problems. Like its two-dimensional cousin, a problem is entered into the
program and field solutions are calculated as described in section § 3.1. Three-dimensional
simulations are appropriate to schemes such as the lDS coil with a target not aligned centrally
so that there is no axial symmetry.
3.3.1 Test Problem
A simple model of an lDS coil with an offset target was constructed to test the effectiveness of
the three-dimensional PEA. The two-dimensional xy-plane model of the cross-section of the
problem geometry is not appropriate since it would assume that the target extended infinitely in
the z-direction and could not simulate the cylindrical coil.
57
Chapter 3
Geometry
As in section § 3.2.1, assumptions about the coil dimensions were taken from a discussion with
the IDS supplier and from the Kaman user manual [10]. The problem geometry is shown in
figure 3.9. The 5 mm thick aluminium target was positioned at d, = 10 mm, had a width 3 times
the IDS coil diameter and was offset from the central position by 0.5 times the coil diameter.
An additional plane was included in the cross-section of the coil to act as a current source. The
outer boundary of the problem space was set to pad all objects by 200 %.
IDS coil --....__ 141 70l ~11 0111 1 cross-section --.........
I
79
Target offset
/ position d, /
t•, .. ~~~~~~~~ 79 o,
y
Target centred position
Figure 3.9. Three-dimensional geometry of the lDS coil and non-centred target yz-plane crosssection. Dimensions given in mm.
Materials
The appropriate materials were selected from the materials catalogue: copper coil
(£, = 1.0000000, ,llr = 0.9999910, a= 5.8000000 X w-7 S.m- 1); aluminium target
(t:,= 1.000000, fl,= 1.0000210, a= 3.800000 x 10- 7 S.m- 1); and vacuum for the remainder of
the problem space(£,= 1.0000000, ,llr = 1.0000000, a= 0.0000000 S.m- 1).
Boundaries
The IDS coil was set to be stranded to prevent eddy currents from forming in it and the current
density estimate from section 2.2 was used to set the total coil current to 0.8 A. This was the
only source in the problem and so the phase was set to zero. The eddy current effect was turned
on in the target and off in the coil.
Solution
The impedance matrix for the three-dimensional solver works in a different way to its two-
dimensional cousin and only objects with external sources can be included in the impedance
58
Chapter 3
matrix; therefore the target was not included, but the coil was. The solution criteria were set so
that the solver used the automatic meshing process with the program's default values of 30%
refinement per pass with a residual of 10- 8• The solver was then set to find a solution with a
maximum error of I %, which took approximately 3 rnin on the computer specified in section
§ 3.1.
Results The impedance of the coil as given by the simulation was found to consist of a resistance of
5.36Ix 10- 5 Q and an inductance of 4.254x 10- 8 H. The inductance value is for a single turn
coil and so these values are in agreement with the estimates found in section § 3 .I .2.
Figure 3.10 shows a plot of the direction of the magnetic field calculated by the simulation.
The vectors show a snap-shot of the field at the start of the current cycle in the coil, which
corresponds to a peak in the field magnitude. On the left-hand side of the coil, the field behaves
in a similar manner to that in figure 3.3 where the field lines appear to be 'compressed' by the
target. To the right-hand side of the target the field behaves differently and there is interaction
with the target where the field appears to curl up at the edge of the target.
./
\ I /
\ I /
Figure 3.10. Magnetic flux direction plotted in the yz-plane of the three-dimensional test problem.
A plot of the magnitude of the z-component of the field taken along a line parallel to the
target, but I mm below the base of the IDS coil, is given in figure 3.Il. On this plot, the
y = 0 mm position corresponds to the point below the centre of the IDS coil. This graph has
59
Chapter 3
some of the same characteristics displayed in the two-dimensional simulation results (figure
3.4): below the edge of the coiiiBzl drops towards zero and outer 'wings' tail off with increasing
distance from the centre. The discontinuities in the plot reveal areas of the mesh that are coarse
and have not produced a smooth field.
4
"' I 0
o+----===~1---------.-------~~-===~~
-200 -100 0 100 200
y /nun
Figure 3.11. Variation in the magnitude of the z-component of the field, IBzl I tesla, with position y I mm, along a line 1 mm below the lDS coil.
The form of figure 3.11 is generally in agreement with the field measurements shown in
figure 2.6, although the central portion below the lDS coil is quite different. This region
consists of two spikes below the edges of the coil and a central dip, which was not observed
experimentally. However, the magnitude of the field roughly agrees with the measured value of
- Sx I 0- 6 T; although the simulation value is slightly lower than the experimental reading.
3.3.2 Simulation refinement
The three-dimensional FEA produced a reliable simulation of the offset lDS coil and target
system. However, the rough nature of figure 3.11 showed that the mesh needed to be refined in
the region between the coil and the target. This is the same effect that was observed with the
two-dimensional simulation where the error for the test problem was also set at 1 %, so it was
thought unlikely that setting this to a tighter tolerance would yield more accurate results.
Therefore a dummy object (§ 3.1.4) was introduced to decrease the mesh size in the region of
interest i.e. the space between the coil and the target. The object was set to be a vacuum to
match the surrounding area, but with a tighter mesh to improve the field solutions. The line
from which the field profile measurements were taken lies 1 mm below the base of the lDS coil
and the dummy meshing space was constructed to include the line with a padding of 2 mm. The
maximum element size in this region was set to 0.5 mm.
60
Chapter 3
The field solution took approximately 90 min to produce a solution to the desired accuracy i.e.
30 times longer than the problem without the additional meshing space. The field profile is
shown in figure 3.12 and comparing it to figure 3.11 demonstrates that the addition of the
dummy meshing object improved the field simulation continuity albeit with a substantial
increase in solution time.
E-"' I 0
~·
2
0+------===T---------,-----~~~-=----~
-200 -lOO 0
"/mm
100 200
Figure 3.12. Variation in the magnitude of the z-component of the field, IBzl I tesla, with position y I mm, along a line 1 mm below the lDS coil, for a geometry with a meshing dummy object.
3.3.3 Parametric Problems
The three-dimensional field simulator did not include the parametric unit that the two
dimensional version did. However, it was possible to use a combination of operating system
batch files and program macros. For example a batch file could include instructions to start the
Maxwell program and execute a macro to construct the problem geometry, set up the materials
and boundaries and solve the problem. Once the program had finished, the next line in the
batch file was executed and a macro containing a different problem geometry could be executed.
General Macro A general macro was developed for use in the later experiments. The macro took the target
distance, d~o target width, W~o and target offset, o, in millimetres from the project file name, as
shown in table 3.1. The format of the geometric parameters was strict, although the final date
tag could be any length to include information about the project date, author, etc. Other
dimensions for the problem geometry were assumed to be constant and were set within the
macro. Using this method the batch file could run a set of problem geometries with differing
problem geometries.
61
Table 3.1. Parameters taken by macro from project file name, where d1 =target distance, W1 =target width, Os= target offset.
General format Example
dr AAAA 0010
BBBB 0222
cc cc 0037
Date or Other Notes DD-MM-YY 01-01-00
Chapter 3
For problems that required dummy meshing objects, a macro was constructed to set the
maximum element size in the problem objects. However, a bug in the Maxwell program meant
that it was not able to utilise macros automatically for the meshing process and a work-around
method had to be used. A batch file called the general macro to construct and set up each
problem. Each problem was then opened individually and the meshing macro manually started.
A second batch file was then used to solve the problems automatically in succession.
Test Problem A parametric test problem was constructed to test the macros and investigate the influence of
target displacement on the impedance of the coil. The general macro and the meshing work
around described above were used. The test problem geometry from section § 3.3.1 was used
with w1 = 222 mm and Os= 37 mm, but the target distance was swept in the range dr = 0, 5, ... ,
25 mm. The mesh was refined such that maximum length of elements in the target and the
measuring gap was 7.5 mm. The whole solution took 450 min, which was approximately 5
times the length of an individual problem, as expected.
The results of the simulation are plotted in figure 3.13 and show the effect described in
equation (1.7) whereby the coil inductance decreases with increasing d1• A further simulation,
with d1 = 50 mm, revealed that the inductance tended to 4.58x 10- 8 H as the influence of the
target decreased. This value differed slightly from the two-dimensional result
(L--+ 4.36x I 0- 8 H), although because the target had very little influence at large displacements,
one would expect them to be identical. This implies that the differences are due to simulation
errors, which cannot be quantified directly since they depend on the particular mesh used for the
solution. None-the-less the difference is less than 5 % and the form of the two- and three
dimensional result plots are as predicted by the equivalent circuit model.
62
oc I 0
4.4
::; 4.2
5
Chapter 3
10 15 20 25
Figure 3.13. The variation of coil inductance, L, with target displacement, d1 for an offset target geometry.
3.4 General Considerations
The FEA simulations of the coil and target system have produced results that compare well with
the experimental observations.
3.4.1 FEA of Experimental Equipment
The simulations discussed above involve idealised models of the coil and target arrangement;
they do not include experimental considerations such as test coils used to measure the field or
spacers used to separate the target and lDS coil.
Test coils
Measurements taken from a system will always affect that system to some extent. In the case of
using test coils to measure the magnetic field, the effect was expected to be negligible since the
coils were stranded and so eddy currents could not form in them. This assumption was
confirmed by completing a two-dimensional simulation of a similar geometry to that of section
§ 3.2.1, but with the incorporation of a test coil. The test coil was modelled as a 5 mm high,
10 mm diameter, empty copper cylinder with an inside diameter of 8 mm, positioned below the
centre of the lDS coil. A plot of the magnetic flux given in figure 3.14(a) revealed no
noticeable change to the field pattern compared to figure 3.3. The magnitude of the z
component of the magnetic field taken along a line located I mm below the lDS coil is given in
figure 3.14(b) and comparison with figure 3.4 also revealed no significant effect from the
addition of the test coil. These results were taken as justification for neglecting test coils in the
later simulations.
63
(a)
Chapter 3
4 ,---------------------------,
": -1------'-~--------==r--~----------l 0
> IO - ; T
JO- GT
J0 - 7 T
< Jo - s T
50 100
R l mm
(b)
150 200
Figure 3.14. Two-dimensional simulation of the lDS coil and target arrangement with a fieldmeasuring test coil. (a) Magnetic flux plot with stronger field represented by lighter colour. (b) Magnitude of the z-component of the field, IB,I I testa, with position R I mm, along a line 1 mm
below the lDS coil.
Plastic Spacers
In the simulations above, the space between the test coi l and the target has been taken as a
vacuum. For the field strengths involved in thi s system, the electrical properties of air were
negligible and so the problem background was modelled as a vacuum. However, for practical
purposes the lDS coil was held above the target using a set of plastic spacers of various heights
to provide an accurate separat ion. It was thought that the non-conducting spacers would not
affect the field since the eddy currents would not form in them. This assumption was confirmed
by completing a two-dimensional simulation based on that described in section § 3.2.1, but with
the incorporation of a plastic spacer. The spacers were machined from clear acrylic block and
the materials catalogue gives the electrical properties of such a material as £, = 3.5000000,
Jlr = 1.0000000, a= 0.0000000 S.m - 1• The width of the block was taken as bei ng that of the
sensor coil and the ax ial-symmetric coordinate system meant that it was modelled as a filled
cylinder positioned directl y below the lDS coil.
A plot of the magnetic flu x given in figure 3.15(a) revealed no noticeable change to the field
pattern compared to figure 3.3. The magnitude of the z-component of the magnetic field taken
along a line positioned 1 mm below the lDS coil is given in figure 3.15 (b) and compari son with
64
Chapter 3
figure 3.4 also revealed no significant effect from the addition of the plastic spacers. These
results were taken j ustification for neglecting plastic spacers in the later simulations.
4
r- 3 _r >C
' ::2 --~I
~ 0
0 50 100 150 200
R l mm
(b)
> J0 - 5 T
I0 - 6 T
I0 - 7 T
< I0 - 8 T
(a)
Figure 3.15. Two-dimensional simulation of the lDS coil and target arrangement with a plastic target spacer. (a) Magnetic flux plot with stronger field represented by lighter colour. (b)
Magnitude of the z-component of the field, IB,I I testa, with position RI mm, along a line 1 mm below the lDS coil.
3.4.2 Edge Effects
The edge effect was noticeable through the initial FEA mode ls, for example in fi gure 3.3 where
there is a fold in the flu x above the edge of the target. This is caused by the eddy currents,
which channel the fi eld around the target object. Thi s process is further demonstrated by the
plot of the z-component of the magnetic fi eld shown in fi gure 3. 16.
65
Chapter 3
Figure 3.16. Demonstration of the edge effect on the z-component of the magnetic field around the target.
3.4.3 Extraction of Data
The output from the magnetic field sensing test coils and the phase-locking program described
in section § 2.6.2 was a single voltage for the entire area of the coil. This signal was the result
of an averaging effect of the flux passing through the coil. The necessity to compare
experimental and simulation results lead to the requirement for a similar averaging effect to be
applied to the simulated field measurements.
The relationship between the incident field and the output from the test coil is a convolution
of the field pattern as a function of position and the response of the test coil as a function of
position. The convolution operation describes the overlap of two functions, which in this case is
between the magnetic field,f(x, y, z), and the test coil's response g (x, y, z). The convolution of
these two functions at a point, p (X, Y, Z), is given by the integral
f ® g = [!(x,y,z)g(x- X, y -Y,z -Z) dx dy dz (3.29)
This describes the three-dimensional case; in two-dimensions the arrangement is the same but
over the coordinates Rand() (or y and z). In the Maxwell programs, field values were extracted
in a convenient format by taking them from a line by the technique used above (e.g. figure 3.4).
To assist in the process, macros were used to draw the lines at the desired positions and then
66
Chapter 3
save the field values to disk. A Java application was constructed to read the data and convolve
them with the coil response function.
For the case of a two-dimensional field solution, lines were constructed to run parallel to the
y-axis (horizontal) over a 5 mm range of 1 mm spaced z-values (vertical). Field values were
taken from the six lines and saved to a series of files with names that described the line
positions. To test the convolution program the coil response was taken as being constant over
the length and width of the coil and coil-field coupling was assumed to be 100 %. The result is
that the coil response function was taken as a step function with fields inside the coil coupling to
the coil and fields outside not coupling to the coil.
In the three-dimensional case, lines were drawn parallel to the y-axis, over a 5 mm range of
1 mm spaced z-values and a 10 mm range of 1 mm spaced x-values. Problem geometries
created by the macro described in section § 3.3.3 produced fields that were symmetrical about
the y-axis. This consideration meant that for test coils positioned on the y-axis, lines only
needed to be drawn on one side of the axis, thereby halving the number of lines to be drawn.
Field values were taken from the 36 lines and again saved to a series of files with suitable
names. As for the two-dimensional convolution, a test was done using a step function to
describe the coupling between the coil and the field.
An example of the three-dimensional convolution is given in figure 3.17, which is the result
of applying the program to the field profile from a small-target simulation. The fluctuations in
the lobes are caused by the edge effect of the target. It can be seen that although the general
pattern in of the filed is unchanged it is smoothed over the area of the test coil. The raw profile
is from a line directly below the centre of the lDS coil, whereas the processed profile takes
contributions from the whole test coil volume. This is responsible for the lower field value in
the central portion of the processed data.
67
f-'0
I 0
2
I I I I
~ --- ---- -- - - - -- - , I \ I \ I 1 I 1 I I I I I I I I
0 ~-----=--.---------.---------~~~--~y
- lOO -50 0 50 100
y /mm
Chapter 3
Figure 3.17. Application of the three-dimensional convolution program to the field profile of smalltarget arrangement. (Solid -) raw field. (Dash --- ) Processed field.
3.5 Summary
In this chapter some of the theory and workings of eddy current FEA have been investigated
and both two- and three-dimensional FEA simulations of an IDS coil and target arrangement
have been developed and refined . The two-dimensional simulations were appropriate for
problems with a large centred target. The three-dimensional simulations were found to take
longer to solve (up to 180 times longer for a solution with a well refined mesh), although they
cou ld be applied to any target and coil arrangement. The models neglected the test coils and the
plastic spacers from the simulations; test simulations were used to justify these assumptions. It
was not possible to quantify the errors on the values produced by the si mulations because the
accuracy of the solution depended on the solver and the nuances of the individual meshes.
Test simulations with d, = 10 mm and w, of three times the IDS coil diameter were completed.
A 2D model was solved with a centred target and a 3D model was solved with Os = 0.5 times the
IDS coil diameter. The simul ations with a refined mesh gave central field values of
2.6 x 10 - 6 T and 2.7 x 10 - 6 T for the 2D and 3D simulations respectively, which were simi lar
in value to the experimentally estimated field strength of- 5 x 10 - 6 T . The coil impedances
were also solved and inductances were found to be 4.051 x 10 - 8 Hand 4.254 x 10 - 8 H for the
2D and 3D cases respectively, which were in agreement with the experimentally estimated
values of- J0 - 7 H. The difference was again due the target offset of the 3D model, which
decreased the coupling and therefore increased the inductance in agreement with the equivalent
circuit models.
Techniques for solving two- and three-dimensional parametric problems have been developed
and were used to demonstrate the influence of target di stance on the impedance of the IDS coil.
68
Chapter 3
The results matched the equivalent circuit models and as d, increased (the influence of the target
decreased) L ~ 4.36x 10- 8 H and L ~ 4.58x 10- 8 H for the 2D and 3D models respectively.
Since at large d, the target had little influence on the coil, the differences between the 2D and
3D models must have resulted from differences in the meshes and solvers. A convolution
program has also been developed to match the output from the field simulations and the signal
measured by the test coils. The results have been compared to experimental results and good
correlation was found.
69
Chapter 4
Inductive Displacement Sensor Limitations
The first chapter's introduction to IDSs and their limitations provides the groundwork for this
present discussion, which concerns results from a complete investigation of these limitations.
This was achieved using the experimental techniques discussed in chapter two and the FEA
electromagnetic field simulations from chapter three. Firstly, the influence of target material on
the lDS is discussed in section § 4.1 where experiments using aluminium, brass, copper, nickel
and steel are described. The following section (§ 4.2) discusses how displacing the target
laterally relative to the lDS coil affects the reliability of the system. This is closely related to
the final section's investigation of the effect of using targets that are smaller than the
recommended 2.5 - 3 times the lDS coil diameter.
4.1 Target Material
IDSs are usually calibrated in the factory for use with a particular target material and attempting
to measure displacements to different target materials will result in errors. The influence of
target material on the impedance of an lDS coil is described in section § 1.4.1 and equation
( 1.13) shows that coil impedance is not only dependent on target displacement and current
frequency, but also on the conductivity and permeability of the target. To investigate this, the
effect of using different materials on the reliability of IDSs was characterised(§ 4.1.1) and the
results were used to show that the effect was real. Earlier equivalent circuit models of the
system were confirmed by modelling the system with FEA electromagnetic simulations
(§ 4.1.2).
4.1.1 Characterising the Effect of Target Material
An experiment was conducted to characterise the effect of using the lDS to measure the distance
to different target materials. The lDS used for the experiment was calibrated for use with an
aluminium target and it was expected that using it on other target materials would result in
errors in the displacement measured.
70
Chapter 4
Table 4.1. Physical properties of some targets investigated.
Sample Width X Thickness I f.lr 0'+ (at 273 Standard Depth of Material Height/mm mm K) /107 Penetration (at 1 MHz) I
±O.Smm ±O.OSmm s -1 .m w-s m
Aluminium 250 X 253 1.50 1.000021 4.00 7.96 Brass 309 X 226 1.30 I 1.59 12.6 Copper 224 X 222 3.30 0.999991 6.45 6.27 Mild Steel 214 X 187 1.00 IOOOt 0.588 0.656 ' Permeability is a function of field 11 = B I H, take I 000 for this estimate. * From Kaye and Laby [39]
Table 4.1 gives the dimensions of the different target samples used in the experiment. The
targets must be of sufficient width to allow eddy currents to flow in the surface as described in
section § 1.4.2. The lDS user manual [10] (p. 15) gives the sensor diameter as 73.7 mm and
since it is unshielded, the target material must be 2.5 - 3 times larger than the sensor. The skin
depth, or standard depth of penetration, was defined in section § 1.2.2 as the point where the
current density has decreased to Ye times its value at the target surface. Table 4.1 gives the
permeability and conductivity, which are used to calculate the skin depth at 1 MHz using the
relation
(4.1)
The distance between the target and the sensor, d1, was varied in 5 mm steps within the range
0- 65 mm. By cycling up and down three readings were recorded and the mean was plotted.
The output voltage was found to vary linearly up to the limit of the sensor range (- 60 mm).
When the target was at a displacement greater than 60 mm the output voltage remained constant.
Figure 4.l(a) shows the displacement to the different target materials as recorded by the lDS.
The axis of abscissas shows the actual target displacement i.e. the physical distance between the
target and lDS barrel. The axis of ordinates shows the target displacement given by the output
voltage of the lDS system. Aluminium was used as the baseline - since the lDS was factory
calibrated with plate aluminium - hence this plot is linear and the actual target displacement
correspond exactly to the lDS predicted target displacement. From the figure it is apparent that
the mild steel sample gave the most error. The brass and copper sample measurements were in
good agreement with the aluminium.
71
6.----------------------------.
> - 4-'5 & ::s 0
Cl 2
0+-----.-----~----~--~----~
10 20 30 40 50 60 Id I 111111
(a)
> g_ g 3.9 Vl 0
40 42
Chapter 4
44 46 48 50 Id I 111111
(b)
Figure 4.1. Influence of target material on lDS displacement measurements. (Solid -) Steel. (Dash --- ) Brass. (Dot ·········· ) Aluminium. (a) Over the whole measurement range. (b) Close-up to
highlight differences.
To highlight the differences between target materials a close-up view for mild steel and
aluminium is given in figure 4.1 (b). Here d1 was varied in 2 mm steps within the range 40 -
50 mm and again, the mean of three readings was found. The two lines have similar gradients
but the steel line is slightly set upwards from the aluminium target. Using linear regression,
expressions describing these straight lines are found to be
Steel: V = 0.087 d 1 -0.049 (4.2)
Aluminium: V =0.091d1 -0.184 (4.3)
each with an R2 value of 0.997. Consider a distance of 10 mm to an aluminium target; this
would produce an output voltage of 0. 726 V. Swapping the target to steel, the same voltage
would correspond to d1 = 9.91 mm, which highlights the problems associated with the influence
of target material.
4.1.2 FEA Simulations of the Influence of Target Material
Using the Ansoft Maxwell 2D program the influence of target material on the magnetic field
was investigated. The two-dimensional module was appropriate because the large centred target
meant that there was axial symmetry. Simulations were completed for each target material at a
range of target distances. The distance between the base of the lDS coil and the top of the target
material was set as a variable that was controlled by the parametric module. The target
materials selected were aluminium, brass, copper and steel as used in the laboratory experiments.
The steel used in the simulations was steel-1008 (plain steel with 0.008 % carbon) which was
chosen because it has similar properties to the sample used in the experiments. A fifth material,
nickel, was also simulated since it does not have a B-H curve (the relative permeability is
72
Chapter 4
constant at 600) and it has a conductivity of 1.45 x 10 7 S.m- 1, thus it was quite different to the
other samples and a worthwhile simulation. A suitable nickel target could not be found for the
experimental testing, but it was listed in the Maxwell 20 material catalogue, which
demonstrated the usefulness of the FEA simulations.
In this model there are two primary position coordinates, which were defined thus: z extended
downwards along the vertical axis and was set to be zero at the base of the IDS coil; and r
extended in a horizontal direction from a zero point at the centre of the IDS coil. The distance
between the base of the IDS coil and the top of the target was denoted by d1 and was positioned
at z = dr.
Simulation Results
The complete parametric solutions to the aluminium, brass and copper problems each took
approximately 15 min, whereas the nickel and steel problems each had a much higher solver
time- 200 min. The FEA software required a finer mesh for materials with a high permeability
than for those with a low permeability. This lead to an increase in the processor time that was
required to solve the large number of elements and the large memory usage increased the
processor time required for swapping page files between the virtual and physical memory.
An example of the simulation results is given by figure 4.2, which shows the influence of
target material on iBzi, the magnitude of the z-component of the magnetic field taken along a line
3 mm below the base of the IDS coil (z = 3 mm), for d1 = 15 mm. All the profiles have similar
forms with a high central portion below the IDS coil and an outer lobe. The aluminium, copper
and brass curves lie over each other and appear identical on the given scale, whereas the steel
and nickel profiles are quite different.
73
3.E-06 -.--------------------,
E- 2.E-06
= ~.
11 ~
::Q' I.E-06
O.E+OO -l------r----,-----,--~:=;==:':::::::::~
0 20 40 60 80 100 R /mm
Chapter 4
Figure 4.2. Influence of target material on the magnetic field, IBz<z = 3 mm)!, from different target material simulations with d1 = 15 mm. R = 0 mm position is directly below the centre of the lDS
coil. (Dash---) Steel-1008. (Dot .......... ) Nickel. (Solid-) Aluminium, copper, brass.
Steel has the highest central field value, which can be explained in terms of the skin effect.
Equation ( 4.1) shows that the high permeability of steel means that it has a low standard depth
of penetration. This decreases eddy currents in the target material and therefore decreases the
field that opposes the incident lDS coil field. Hence the field below the lDS coil is not
counteracted to the same extent that it is with lower-permeability materials. This is further
illustrated by the plot of central field values given in figure 4.3. With increasing d, the
aluminium and steel curves meet as the influence of the target decreases. But more importantly,
it is noted that the steel target gives a lower spread of central field values, which results from the
skin effect.
3
E-'C --- ---·
I
0 2
= "" 11
'" 0 11 ~ cz:l'
0
0 20 40 60 80
Figure 4.3. Variation in central field value, IBz<r=O, z=3)1, with target displacement, d1• (Dash --- ) §teell-1003. (Dot .......... ) Niclkei. (Solid-) Alumiunium, coppe1r, lln·ass.
74
Chapter 4
The influence of target displacement on the IDS coil impedance is shown in figure 4.4. With
increasing target displacement, the resistance decreases and the inductance increases, which is
in agreement with the equivalent circuit equations (1.8) and (1.9). It can be seen that with
nickel and steel targets the effect is substantially different to aluminium, brass and copper.
15.-.------------------------,
3.9 c: 10 :r:
X
0 s 3.7
', "~ ........ 3.5
<:1:: 5
3.3 +-_L_-------,-------------.----------,---'
20 40 60 0 20 40 60 d,lmm d,lmm
(a) (b)
Figure 4.4. Impedance components as a function of target displacement, d1• (Dash --- ) Steel-1 008. (Dot .......... ) Nickel. (Solid-) Aluminium, copper, brass. (a) Resistance, R. (b) Inductance, L.
Edge Effects
The edge effect was introduced in section § 3.4.2 as the channelling of the magnetic flux around
the edge of the target. Interestingly, the strength of the effect depends on the target material and
it is weaker for steel (figure 4.5(a)) than it is for aluminium (figure 4.5(b)). Note that in these
figures, the axis of abscissas starts at R = 35 mm, which corresponds to the edge of the IDS coil,
so these plots only show the external lobes. It might be expected that the higher permeability of
steel would increase the field channelling and thus increase the edge effect, however the higher
permeability also leads to a smaller skin effect and the edge effect is reduced. This effect has
important implications for electromagnetic shielding and is discussed by Marsh and J ohnstone
[40]. The edge effect decreases with target displacement and it was found that in general when
the target was at d, > 30 mm, the edge effect could not be distinguished from the background
field.
75
10
f-
' 0 - 5 - I
~
0
35 85 135
Rlmm
(a)
185
f- 7.5 ~
' = 5
<>:i' -2.5
35 85
Chapter 4
135 185
Rlmm
(b)
Figure 4.5. Dependence of edge effect on target material demonstrated by the field plotted along a line 1 mm below the lDS coil. (a) Aluminium. (b) Steel.
Further Investigations
Note from figure 4.2 that the form of the field profiles is the same regardless of the target
material, however the central and outer lobe field values do change. Some further simulations
were completed to investigate this fully and explore whether or not it provides more information
about the target. Since the results for non-ferromagnetic materials were very similar, aluminium
was arbitrarily selected for the further simulations with the assumption that it was also
representative of copper and brass. Models were constructed to find a target displacement
where IB~(r = 0, z = 3)1 matched for both steel and aluminium targets. Since the aluminium
problems were faster to solve, the displacement of aluminium was varied to match the field to
that of existing steel results. Three different values of IBir = 0, z = 3)1 were selected from
previous steel simulations and for each a series of new aluminium results were found to home in
on a target displacement with the same central field value. During each of the simulations
impedance values were also calculated and the results are shown in table 4.2.
Table 4.2. Influence of target material on lDS coil impedance.
IB~(r = 0, z = 3)~/ T Sam~le Material d1 /mm R/10 "n L 110 sH
2.316x 10 Steel-1008 20.0 0.448 3.976 Aluminium 28.2 7.279 3.944
2.405 X 10 6 Steel-1008 25.0 3.685 3.975 Aluminium 32.9 7.211 3.968
2.467x 10 6 Steel-1008 30.0 2.826 4.000 Aluminium 37.8 7.145 4.002
It was found from plots of the results that matching the central field values also matched the
lobe values and so the profiles were identical. This meant that it was only the magnitude of the
field that changed with target displacement and not the shape of the field. This implies that
76
Chapter 4
looking at the field profiles in this way cannot provide any more information about the target
material than is already available from the coil impedance.
41.1.3 Target Material Summary
The influence of target material on the output from the IDS has been investigated and it has
been shown that this is a real problem. FEA simulations have been completed for a range of
target displacements to several different target materials. Investigation of the coil impedance
matrix confirmed that the simulations were in agreement with the theoretical equivalent circuit
treatment of the system. Further simulations to match the magnetic field profiles of different
target materials revealed that it is just the magnitude of the field that changes with target
displacement and not the shape of the field. The coil impedance and field are not independent
variables and so this method can not reveal any more information about the target. In summary,
a target-independent IDS cannot be realised by measuring the magnetic field in this way.
4.2 Target Offset
In section § 1.4.3 the influence of target offset on the reliability of inductive eddy current
displacement sensors was introduced. From an empirical point of view, as the target offset
increases one expects the reliability of the IDS to decrease, that is, the target displacement and
output voltage will no longer be linearly related. This section shows how this effect was
investigated; the limitation was characterised experimentally and theoretically (§ 4.2.1), the set
up was modelled with EM FEA simulations (§ 4.2.2) and experiments were used to confirm the
results ( § 4.2.3).
4.2.1 Characterising the Effect of Target Offset
The influence of target offset on the output of an IDS was investigated with an experimental
characterisation. The target material was set at a fixed displacement and the IDS output voltage
was recorded for different lateral displacements. The target displacement was then changed and
a new set of readings was taken.
The target width was fixed at 2.6 times the IDS coil diameter since this is of sufficient size to
avoid the edge effects from too small a target width. The Kaman IDS under test was calibrated
with aluminium and so this was the logical choice for the target material in these experiments.
The results of the previous chapter reveal that the results are similar for materials with a low
permeability and so aluminium is a good representation of copper and brass targets too. The
target was cut from 5 mm thick plate, which is much larger than the skin depth (see table 4.1 ).
77
Chapter 4
The thickness also increased the consistency of the results, since it meant that the target was flat
as it did not distort as readily as thinner samples.
The IDS and target were separated by non-conducting spacers and three experiments were
conducted with target displacements of 10, 20 and 30 mm. Figure 4.6 shows the results and
gives the output of the IDS in terms of the percentage error in predicted target displacement.
This is simply defined by
dt(IDS) -dt %distance error= x 100
dl (4.4)
where d1rws1 is the target displacement that corresponds to the recorded IDS output voltage,
whereas d1 is the actual target displacement. The results confirm that the output from the IDS
becomes less reliable as the target offset increases. Note that small errors for d1 = 10 mm at low
offsets are a result of experimental errors where very small changes in voltage lead to a
percentage distance error of - 1 %. As increasing offset leads to the coil and target edges
aligning at - 0.8 times the IDS coil diameter the error becomes large and beyond this point the
readings are highly unreliable. The lower the target displacement, the larger the offset could be
without affecting the IDS output. However, higher target displacements were found to have a
lower error at higher offsets. For offsets larger than those shown in this figure, the curves
reached plateaux when the target no longer has an influence on the IDS.
100
.... 2 75 .... d)
d) u c: r3 50 "' :a
&. 25
0 0 0.4 0.8 1.2
o, I IDS coil diameter
Figure 4.6. Influence of target offset on lDS output. Normalised lDS output with target offset, o., at different target displacements, d1• (Solid -) d1 = 10 mm. (Dash --- ) d1 = 20 mm. (Dot .......... )
d1 = 30 mm
78
Chapter 4
4.2.2 FEA Simulations of an Offset Target
The results of the previous section reveal that the IDS coil is affected by target offset, but
further investigations were required to determine the reasons for the effect. FEA simulations
were completed to determine the patterns of the field around the IDS coil. A three-dimensional
geometry was used since the influence of the target on both sides of the IDS coil was of interest
i.e. the influence of the advancing target edge and the receding target edge. Using the
parametric methods described in section § 3.3.3, geometries were constructed with target offsets
os= 0, 5, ... , 150 mm for target displacements d, = 10, 15, ... , 30 mm.
Figure 4.7 shows the influence of large offsets on the field profiles. As the edge of the target
moves below the IDS coil, the magnitude of the field below the coil increases. This is because
the influence of the eddy currents decreases and therefore the IDS coil field is not counteracted
to the same extent as when the target lies directly below the coil.
3 ,------------------------------------,
E- 2 "' I 0
ex:)" 1
o~~~~~~--~----~~~~~
-1.5 -1 -0.5 0 0.5 1.5
y I lDS coil diameter
Figure 4. 7. Field profiles for large offset targets ford, = 10 mm. (Solid --) Os = 0 mm. (Dash---) Os= 100 mm. (Dot .......... ) Os= 100 mm. (Dash dot-·-·) Os= 125 mm. (Dash dot dot_ ... )
Os= 125 mm.
More practical use can be made of the results of smaller offset models as shown by the
example field profiles with offsets Os= 0, 20, 40, 60 mm that are given in figure 4.8. Figures
4.8(a)- 4.8(d) show the field profiles ford,= 10 mm and figures 4.8(e)- 4.8(h) show the field
profiles ford,= 30 mm. Note that the axis of abscissas focuses on the lobe regions and is scaled
in terms of the IDS coil diameter (72 mm) e.g. the edge of the coil corresponds to y = 0.5.
Particular attention should be paid to the variations in the field for the same offset, but different
target displacements. For large target displacements, the d, = 30 mm plot contains just one lobe
that decreases in magnitude with increasing target offset. The peak of the lobe remains at the
79
L________________________________________________________________ -- -
Chapter 4
same position, independent of the offset. However, the d, = 10 mm field includes three lobes
and the middle lobe is drawn to the left as the target edge advances. The difference between the
d, = 10 mm and d, = 30 mm field profiles is a result of the target edge effect, which was
discussed in section 3.4.2.
Os! d1 = lOmm d1 =30mm mm
12 12
,.... 8
,.... 8
' ' 0 0 - -- -0 ~4 ~4
0 0 0.4 1.6 2.2 2.8 0.4 1.6 2.2 2.8
y I lDS coil diameter y I lDS coil diameter
(a) (e) 12 12
,.... 8
,.... 8
~
' ' 0 0
~ - -- -
20 ~4 ~4
0 0 0.4 1.6 2.2 2.8 0.4 1.6 2.2 2.8
y I lDS coil diameter y I lDS coil diameter
(b) (f) 12 12
,.... ~
8 ,....
8 ' ' :::: 0 - -- -
40 ~4 ~4
0 0 0.4 1.6 2.2 2.8 0.4 1.6 2.2 2.8
v I lDS coil diameter v I lDS coil diameter
(c) (g)
80
12,--------------------------~
:-- 8
60 ~:~l/~ 0.4 1.6 2.2 2.8
y liDS coil diameter
(d)
Chapter 4
12,--------------------------~
:-- 8 ' 0
~4
~ 0~--~----~==~====~
0.4 1.6 2.2 2.8
y liDS coil diameter
(h)
Figure 4.8. FEA simulations of offset targets at different target displacements. (a)- (d) d1 = 10 mm. (e)- (h) d1 = 30 mm.
Figure 4.9 shows the influence of target offset on the lDS coil inductance for different target
displacements. With increasing offset, the curves converge to a point as the influence of the
target diminishes. These results are in agreement with the equivalent circuit model described by
equation ( 1. 9), which shows that closer targets result in a lower lDS coil inductance because of
the stronger coupling to the target.
00
I
4.5 .--------------------------------------------.,
0 4.25
4+-----------,-----------,-----------~
0 0.4 0.8 1.2 os I IDS coil diamater
Figure 4.9. Influence of target offset on coil inductance. (Solid -) d1 = 10 mm. (Dash --- ) d1 = 20 mm. (Dot ·········· ) d1 = 30 mm
Figure 4.10 shows the change in coil impedance and lobe amplitude with target offset. Recall
that the lDS measures target displacement only using the coil impedance.
81
Chapter 4
.--------------------,- 4.44
4.4 ;--6
I
0
:r: oc
I
4.36 0
-l
4.32
2 +---,,-------,---,---,-------,--....,---'- 4.28
0 0.2 0.4 0.6 0.8 1.2
Offset I IDS coil diameter
Figure 4.10. lDS coil impedance and magnetic field lobe amplitude for d1 = 30 mm. (Left, solid -) Lobe amplitude. (Right, broken --- ) IDS coil inductance.
4.2.3 Experimental Measurements of an Offset Target
The results of the previous section were confirmed by experimentally measuring the output
from the lDS taking test coil readings at the same time. For d1 = 25 mm and with a target width
of 3.3 times the lDS coil diameter, the target was offset and readings taken. The results are
given in figure 4.11, with the test coil output scaled such that a value of I corresponds to the
reading with no offset and the lDS output scaled to give the percentage distance error.
.... 5. :; 0
:g 0.8 u .... "' 2
"0 0.6 V
"' ~ § 0.4 z ---0.2 -!""-'~"--;.---'"""-=r-=-=-o...:-=-=j-'-=_"-'_=-=_'--'_T--_--,-----,-------'-
0 0.2 0.4 0.6 0.8 1.2
Normalised sensor coil offset
12
10
..... 8 0
!:: 0)
0)
6 u c: .:s "' :a
<>'<
2
0
Figure 4.11. Experimental confirmation of FEA simulation results. (Left, solid -) Normalised test coil signal. (Right, broken --- ) lDS distance error.
4.2.4 Target Offset Summary
The influence of target offset on the output of the lDS has been characterised and was shown to
be a real problem that leads to a decrease in reliability of the measurements from the system.
82
Chapter 4
The lower the target displacement, the larger the offset could be without affecting the IDS
output. However, higher target displacements were found to have a lower error at higher offsets.
FEA simulations were conducted and the results were found to agree with experimental
measurements. It is proposed that by using an array of small test coils around the IDS it would
be possible to compensate for the influence of target offset on the IDS output. The relationship
between the lobe shape and amplitude is not trivial and either a look-up table or a trained
artificial neural network could be utilised to convert test coil measurements into an IDS
correction factor. In this way, the influence of target offset on the output from an IDS could be
corrected, which would result in more reliable displacement measurements.
4.3 Target Width
The influence of target width on the output from an IDS was introduced in section § 1.4.2 and is
closely related to target offset. In this section the effect of using targets smaller than the
recommended width is investigated, which begins with a characterisation of the effect in section
§ 4.3.1, where it is shown that the problem is real and the resulting measurement errors are
calculated. The results of FEA simulations are presented in § 4.3.2 and conclusions are drawn
in section § 4.3.3.
4.3.1 Characterising the Effect of Target Width
The influence of target width on the output from the IDS was characterised experimentally. As
in the previous section, aluminium plate targets with a thickness of 5 mm were used since the
IDS was factory-calibrated for this material; the thickness targets ensured a flat surface for the
experiment. Two experiments were completed: the first measured influence of target size on the
IDS output voltage for a fixed target displacement; the second concerned using the IDS to
measure the displacements to different target widths. For both experiments, target
displacements were controlled with non-conducting plastic spacers.
The target was maintained at a constant displacement, d1 = 20 mm and the output from the
IDS was measured with different target widths. The targets used in the experiment were as
follows: 2.6, 2.4, ... , 1.2, 1.0 times the IDS coil width. As the effects were observed to increase
sharply as the target size approached the diameter of the IDS coil, an additional target was
constructed with a width of 1.1 times the IDS coil width. Figure 4.12 shows the results from the
experiment, from which it can be seen that as the target width increases, the accuracy of the IDS
increases. The curve levels out, which shows that using a target wider than about 2.5 times the
IDS coil diameter does not improve the IDS accuracy.
83
1.75 > '5 %1.65 0
r/J
e 1.55
1.5 2 2.5
W 1 I IDS coil diameter
Figure 4.12. Influence of target width on the lDS output.
Chapter 4
In the next experiment, three target sizes were investigated: 2.6, 1.4 and 1.2 times the IDS
coil width. For each target, the output from the IDS was measured at different target
displacements. The results are shown in figure 4.13, from which it can again be seen that the
IDS reliability deteriorates with decreasing target width. Figure 4.13(a) shows that the linearity
of the system is dependent on the target width and displacement. Smaller targets give reliable
results at lower target displacements and it is only when the target is moved further away that
the output deviates from a linear response. By comparing the measured voltage with the output
that would be expected at a given target displacement, a measure of distance error can be
obtained, which is defined by equation (4.4). This error is plotted for target displacements
larger than 25 mm in figure 4.13(b ).
6 30
5 25 > 4 -5 3 & :::l
2 0
"' 9 I
:s po V
~ 15
~ 10 ~
0 5
-I 0 0 10 20 30 40 50 25 30 35 40 45 50
d 1 1mm d, /mm
(a) (b)
Figure 4.13. Influence of target width on the lDS output. (Solid -) w, = 2.6. (Dash --- ) w1 = 1.4. (Dot··········) w, = 1.2. (a) Non-linearity introduced with different target widths. (b) Distance
measurement error resulting from small target widths.
84
Chapter 4
4.3.2 FEA Simulations of the Effect of Target Width
Using Ansoft's Maxwell 3D program, the influence of an offset target on the field around the
lDS was investigated. The three-dimensional module was selected because as the width of the
target decreased, the influence of the corners increased and so the approximation that the target
was axially symmetric -as had to be assumed in two-dimensional simulations -increased the
modelling error to an unacceptable level. Two groups of simulations were run: one with
d1 = 10 mm and another with d1 = 20 mm. For each group, nine simulations were run with each
having a different target width.
Some results from the FEA simulations are presented m figure 4.14, which shows the
influence of target width on the field profiles. Figures 4.14(a) -4.14(c) are for a target
displacement of d1 = 10 mm and figures 4.14( d) - 4.14( e) are for a target displacement of
d1 = 20 mm. Comparing these figures with figure 4.7, highlights the difference between the
influences of target offset and target width. As has been explained in previous sections, the
central portion of the field, below the lDS coil, is reduced in magnitude for a lower target
displacement. The influence of an offset target is to skew this central portion, whereas a small
target width gives a skewed effect for both sides and the result is a central dip. This is less
prominent at higher target displacements, which indicates that it results from the edge effect that
was described in section § 3.4.2.
The influence of a small target width on the outer lobes is similar to that observed for an
offset target. At small target displacements, the edge effect causes the outer lobes to be broken
into separate lobes. However at large target displacements, this effect is not present and there is
a single lobe that decreases in magnitude with decreasing target width.
W 1 f IDS dia
15
f-
'7 10 0
2.6 cci' 5
d1 = 10 mm
0+-~~--~--------~---r~~
-1.5 -I -0.5 0 0.5 1.5 y I lDS coil diamter
(a)
d1 =20mm
15
f-,_ 10 I
s --cci' 5
0
-1.5 -I -0.5 0 0.5 1.5 y I lDS coil diamter
(d)
85
Chapter 4
15 15
f- f-~
10 ~
10 ' ' 0 = - -- -1.8 ~, 5 ~5
0 0
-1.5 -1 -0.5 0 0.5 1.5 -1.5 -1 -0.5 0 0.5 y I lDS coil diamter y I lDS coil diamter
(b) (e)
15 15
f- f-';- 10
~
10 '
= 0
- -- -1.0 ~- 5 ~5
0 0
-1.5 -1 -0.5 0 0.5 1.5 -1.5 -1 -0.5 0 0.5 y I lDS coil diamter y I lDS coil diamter
(c) (f)
Figure 4.14. FEA simulations of the influence of target width on the magnetic field. (a)- (d) d1 = 10 mm. (e)- (h) d1 = 20 mm.
4.3.3 Target Width Summary
1.5
1.5
The use of small targets on the output from IDSs has been characterised and it was shown that
there is a real effect on the reliability of the distance measurements. The effect is similar to that
of an offset target and at low displacements the target affects the lobe shape. A similar array of
test coils that was proposed to measure an offset target could also be used to counter the
influence of target width.
4.4 Summary
In this chapter the techniques developed previously were applied to investigate the limitations of
IDSs. The test coil design that was described in chapter two was applied to measure the field
around the test coils experimentally and the FEA methods discussed in chapter three have been
utilised to simulate these fields. A combination of two- and three-dimensional FEA simulations
have been used to investigate the influence on the lDS output of target material, target offset
and target width.
The effect of target material on the lDS was demonstrated by obtaining two equations for the
measured voltages and the corresponding target displacement: for steel V= 0.087d,- 0.049 and
for aluminium V= 0.091 d, - 0.184, each with an R2 value of 0.997. Solutions for steel and
86
Chapter 4
nickel problems took approximately 13 times longer than aluminium, brass and copper targets.
The field profiles for aluminium, brass and copper overlapped and with d1 = 5 mm, the
iBz(r = 0, z = 3)1 values were 3.07 X 10- 7 T. The values were 6.15 X 10- 7 T and 1.49 X 10- 6 T
for nickel and steel respectively. The difference resulted from reduced coupling to the higher
permeability materials, which is a consequence of the skin effect. As d1 - oo and the influence
of the target material decreased, the central field values all tended to the same value of
2.53 x 10- 6 T. Further simulations showed the edge effect was stronger for an aluminium
target than a steel target. The impedance results were observed to follow the equivalent circuit
models. Further steel and aluminium simulations were ran to match the central field values.
This was also found to match the lobe amplitudes and so it was determined that monitoring the
lobes did not reveal more information about the target material.
The influence of an offset target on the reliability of an IDS was investigated experimentally
and with FEA simulations. An experimental characterisation of the influence of offset revealed
that the lower the target displacement, the larger the offset could be without affecting the IDS
output, but conversely that higher target displacements yield a lower error at higher offsets. For
example with os= 1.23 times the IDS coil diameter the distance errors were 107, 70, 58% for
d1 = 10, 20, 30 mm respectively. FEA investigations showed that the impedance of the IDS coil
followed the behaviour described by the equivalent circuit equations. The value of the
simulated impedance with the target at a large offset was approximately 20% larger than for the
same experiment conducted in 2D for the material investigation.
The target edge effect was found to play an important part in shaping the lobes at low target
displacements. At low target displacements the field external to the IDS was found to comprise
a number of distinct sub-lobes, whereas at higher target displacements only a single lobe was
found. By monitoring the lobe amplitudes with a test coil array it was found that the effect of
an offset target could be corrected. For example, with d1 = 25 mm and W 1 = 3.3 times the IDS
coil diameter, when Os= 1.2 times the IDS coil diameter the distance error was 3.6 %, which
corresponded to a normalised test coil output of 0.54.
The influence of target width on the IDS was demonstrated to be similar to that of target
offset and edge effects were again important at low target displacements. It was proposed that
the lobes could be monitored using an array of test coils and either a look-up table or an
artificial neural network could used to compensate for the affects of target offset.
87
Chapter 5
Conclusions
The primary aim of the work described in this thesis was to investigate the limitations of
inductive proximity sensors and it was initially proposed that measuring the field external to an
IDS could provide more information than was available from the lDS coil impedance alone.
The first chapter included a general discussion about displacement sensing and applications
where different technologies are appropriate. Particular emphasis was placed on comparing
behaviour in harsh environments where dust, dirt, oil, humidity, etc. can interfere with the
measuring process. This discussion lead to the confirmation that IDSs were suitable for making
displacement measurements in harsh industrial environments and that they had advantages over
other technologies that could not perform as well in these conditions. The discussion of lDS
operating principles lead to an understanding of their limitations and it was shown that target
material, offset and width affected the sensors. IDSs have been widely used in industry for a
number of years and many systems are available commercially, consequently it was determined
that an investigation of their limitations was an important physical problem.
The field around the IDS coil was found to be sinusoidal with a magnitude - I 0- 6 T and a
frequency of I MHz. A comparison of magnetic sensing technologies in the second chapter
determined that a number of devices are available that can measure a field with these
characteristics although many - such as SQUIDs - would be impractical for the application
environment. A simple test coil was shown to be the most appropriate device for this
application, although a phase locking signal processing technique was required to produce a
high signal to noise ratio at low field strengths ( < 2 x 10- 6 T). Before processing, an example
signal was found to have a mean amplitude of 4.65 x 10- 4 V with a variance of 4.36 x 10- 7 V2,
but the phase-locking technique revealed an amplitude of 0.0324 V with a variance of
l.I2 x 10- 7 V2. Hence a system was developed that could reliably measure the magnetic field
around the lDS coil.
The third chapter described work to simulate the magnetic fields around IDSs with
commercial FEA software. Both two- and three-dimensional models were constructed, tested
and refined to produce smooth field values. Central field values produced by the 20 and 3D
models were 2.6 x 10- 6 T and 2.7 x 10- 6 T respectively, which matched the experimentally
88
Chapter 5
measured value of- 5 x 10- 6 T. Also, investigation of the influence of target displacement on
the impedance of the lDS coil found the behaviour to match with the equivalent circuit models.
Hence the simulations were shown to be an accurate model of the experimental equipment. A
program, that was developed to convolve the simulated field and test coil response, was found
to improve the match between experimental and simulation results and the result was a system
suitable for the investigation of limitations of lDS systems.
The effect of target material was shown to be real experimentally by calibrating the lDS,
which was demonstrated by the two relations: V= 0.087d1 - 0.049 (for steel) and V= 0.09ld1 -
0.184 (for aluminium), each with an R2 value of 0.997. Simulations were setup that produced
impedance values that agreed with theoretical models. These simulations showed that the field
profiles of aluminium, brass and copper were very similar and when d1 = 5 mm, the
IBzCr = 0, z = 3)1 values were 3.07 x I 0- 7 T. For nickel and steel, the values were 6.15 x 10- 7 T
and 1.49 x 10- 6 T respectively. This demonstrated how the permeability of the target material
affected the lDS field. Further simulations were completed to investigate this further and it was
found that varying d1 to match the central field values also matched the lobe amplitudes. This
meant that it was not possible to reduce the target dependence by monitoring the field in this
way.
The target offset effect was demonstrated experimentally by measuring the distance error with
offset. For example when Os= 1.2 times the lDS coil diameter, the distance errors were 107, 70,
58% for d1 = 10, 20, 30 mm respectively. This showed that the target offset effect was a real
problem that could potentially have made measurements highly unreliable. FEA simulations
revealed the effect of the offset targets on the magnetic field around the lDS. Agreement was
found between the simulated and theoretical coil impedance variations, which confirmed the
appropriateness of the model. The external field lobe on the side nearest the leading offset edge
was affected while the trailing edge was unaffected. Two key features in the leading edge lobes
were observed: the amplitudes decreased with increasing offset and at low target displacements
the edge effect caused the lobes to split. An experiment with the test coil array confirmed that it
was possible to use the change in lobe amplitude to measure the offset of the target, for example
when d1 = 25 mm and w 1 = 3.3times the lDS coil diameter, with Os= 1.2 times the lDS coil
diameter the distance error was 3.6 %, which corresponded to a normalised test coil output of
0.54. Hence it was possible to correct the output signal from the lDS coil to counteract the
effect of an offset target.
Target width was found to have a similar effect to target offset. Again, experiments were
completed which showed that the effect was a real problem, for example with d1 = 20 mm when
89
Chapter 5
w1 = 1.2 times the lDS coil diameter, the output was 8 % larger than it was when w1 = 2.5. FEA
simulations showed that both sides of the lDS external field lobes were affected by the smaller
target compared to just one side with an offset target. The same features were observed in the
field lobes: the amplitudes decreased with increasing offset and at low target displacements the
edge effect caused the lobes to split. Hence it was possible to measure the lobe amplitudes and
correct the lDS output to compensate for the target width effect.
Future work could develop the test coils further and produce an array suitable for use in harsh
environment applications. Also, the target offset and width corrections could be developed with
the use of either look-up tables or artificial neural networks to utilise the lobe splitting that was
caused by the edge effects.
The macros and the convolution program were very versatile and future work could utilise
them as they could easily be adapted to use new geometries and materials. The experiments for
the effect of target offset and width only looked at aluminium targets, which were taken to be
representative of targets with a low permeability. Steel targets were not simulated because of
the time taken to produce solutions, which was a consequence of the large mesh sizes. Future
work could complete these experiments on a more powerful computer. A further parameter that
could be investigated is target thickness; simulations could be run to see the effect of using
targets approaching the skin depth. This could also be achieved by modifying the macros.
The frequency of the lDS coil that was simulated was fixed, however the skin effect was
dependent on the frequency of the exciting radiation and so simulations involving different
frequencies or a burst of frequencies would be worthwhile.
When measuring the magnetic fields, only the magnitude of the test coil signal was measured.
In practical experiments phase information was lost in the signal processing program and in the
FEA simulations the phase information was not collected by the macros and convolution
program. Further work could investigate the effect of the parameters on the phase of the test
coil signal.
90
Appendix 1
Published Research
The paper "Improving the Reliability of Eddy Current Distance Measurements with Finite
Element Modelling" by M. R. Wilkinson and S. Johnstone was taken to The Institute of Physics
Sensors and their Applications XII conference in Limerick, Republic of Ireland in September
2003. It is published in the book Sensors and their Applications XII (0750309748) by Institute
of Physics Publishing in 2003. It is reprinted here with permission.
91
Appendix 1
IImm JP) Jr@ vnlillg lllhl ~ IRtellnSllbl iillii lly @it' IE<dl dl y CC unJrlrtelillll JI))Ji§lt311ill <e~ M~Sl§lilllr~m~lillll§ wnlllhl IFniDliillte IEllem~Il1lll M@dl~llllniDlg
M. R. Wilkinson, S. Johnstone
School of Engineering, University of Durham, South Road, Durham, DH1 3LE, United Kingdom
Abstract: Eddy current distance measuring devices are used widely in a number of harsh environment applications. However they have limitations and this paper looks at the effect of non-centred targets on the reliability of such devices. It was found that when a target was offset by 1.3 times the sensor coil diameter there was an error of 6.5% in the distance measured.
Finite element electromagnetic field simulations have been employed to model the system and have shown how the field outside the sensor coil changes with target offset. By monitoring this field with small test coils it is possible to correct the distance measurement error. This work has potential to lead to an improvement to the range of applications in which eddy current distance measuring devices may be employed.
1. ][ntrodu.nction
Eddy current sensors (ECSs) [1] are widely employed to measure the distance to conducting targets in harsh environments [2]. Such true position measuring devices comprise a sensor coil and associated electronics. An alternating current is passed through the coil to generate an electromagnetic field. When a conducting target material is placed in this field, eddy currents are generated which produce an opposing field thus reducing the original intensity. This causes an impedance variation in the sensor coil which is detected by the monitoring electronics. The distance to the target is given as a voltage that is directly proportional to the target displacement. Non conducting materials between the ECS and target will not affect the field and so they can operate in environments where dust, oil or humidity, etc. are present. This is a major advantage over other distance measuring devices.
The distance range over which an ECS will provide linear results is directly proportional to the diameter of the ECS coil. The magnetic field around ECSs with a shield is less extended than for unshielded designs. This has the effect of reducing the measuring range, but means that smaller targets may be used. For shielded ECSs the target size should be at least 1.5 to 2 times the ECS coil diameter and for unshielded ECSs the target should be at least 2.5 to 3 times the ECS coil diameter [3]. Using a target size smaller than these limits reduces the linearity and long term stability. A similar effect is observed when the target is offset from centre; that is the target extends a greater distance on one size of the ECS coil than on the other. Previous authors have looked at various aspects of ECS reliability [4, 5], but this paper summarises research into a solution to the offset problem and is a subset of wider work on the limitations of ECSs.
92
Appendix 1
Experimental work was carried out using a commercially available eddy current distance measuring device from Kaman Instrumentation. This enabled the researchers to avoid the complication of constructing and fine-tuning such a device [6] and meant that the limitations of a well calibrated system were investigated. The system was modelled using Ansoft's Maxwell3D™ finite element electromagnetic field solver using an eddy current module; this is detailed in section two. The results of these simulations have been confirmed experimentally (section three) and section four shows how they were interpreted and exploited.
2. Simulation of Target Offset
There are a number of modelling methods through which more can be learnt about electromagnetic sensor designs. Early analytical work on shielding and eddy current problems [7, 8] is relevant but limited to simple geometries. Probable flux methods [9] are suitable for complex geometries, but often require large assumptions. However with increasing computing power rigorous numerical finite element methods [ 10, 11] have proven to be useful in three dimensional and high frequency cases [12].
The ECS coil was modelled as a 1 mm wide rectangle swept 360° around a central axis with an alternating current source running at 1 MHz. The magnetic field strength was measured below the ECS coil using a test coil. By treating it as a solenoid, the amplitude of the current in the coil was estimated. This value was then adjusted so that the simulated field strength matched the measured field strength. The ECS coil was located above a square aluminium target that was positioned with various offsets relative to the ECS coil as illustrated in figures 1 (a) and 1 (b). The target material had a width of 3 times the ECS coil diameter and a thickness of 5 mm. The distance between the ECS coil and the target was fixed at 20 mm.
Finite element field solutions were computed on a fine mesh and the magnitude of the magnetic field in the direction along the ECS coil axis (z-axis in figure 1), IBzl, was measured on a line perpendicular to the ECS coil axis (y-axis in figure 1) in the region between the ECS coil and target.
--+-+-'Y
r . r dLY~
r ! r ITL~~
====
(a) (b)
Figure 1. Wire frame perspectives of the problem geometry for (a) a target offset of zero and (b) a target offset of 0.6 times the sensor coil diameter.
93
l.SE-06
1-.::; l.OE-06 ~
S.OE-07
-1.5 -1 -0.5 0 0.5 1.5 Position I ECS coil diameter
(a)
Appendix 1
2.0E-06 ,...---------------,
1.5E-06
1-.::; l.OE-06 ~
5.0E-07
O.OE+OO +. ----,-----'T----.-~r"---"--,.----1
-1.5 -1 -0.5 0 0.5 1.5 Position I ECS coil diameter
(b)
Figure 2. The field profiles for (a) a target offset of zero and (b) a target offset of 0.6 times the sensor coil diameter.
The field was found to consist of a higher central portion immediately below the ECS coil and two 'lobes' to either side. As the offset was increased (i.e. the ECS coil was displaced laterally relative to the target centre) the lobe on the side closest to the advancing target edge decreased in magnitude and was curtailed in its lateral extension. This is illustrated in figure 2 which shows the field patterns for an offset of zero and an offset of 0.6 times the ECS coil diameter.
''''''"' \\\ ,,,, \\'\\'-.'-.\\' \\\} ~\ ZL '\'\\\\\'-\ ~111 \\\\\\\\ 11\\
\\\\\\\\11)1111 1\\\\11111 I 11 \ I I l I I 1. I I I I. I I I I Y l.l!IJil!.JIIIfllllll,l·l· ... I. I f I I I I I I I I I I I / ll!llllllilllllt!il// llil!lll/;//;till//// il//ll/11////lll///// ///////1////////----~ ////////////// ..... -~-----~---·
\,,,,,~-------~-- -~
~ ''';;;:::;:,;, ~;s§"lsfflT:I!p;mJarget::::::::: (a)
-,,,,,,,,\' \\\\ ZL '''''"''''''' , ..... ' '\ '\ ' \\' \ \ \ ~ \ \
. \('\'\\\\\\\\\\\\ \1\l\\111\\\\ll \ I \1 I I l I I I. I I \ l
I I I I I I I I I I I 11. I I I Y ) f f ) f I I. I I I I I ';' I I I I 1 I I I. I I I I, I I I I I I I I /. I I I I I I I i 1 1 I r1 I!;/ 1 /; 1 1 I 1 1 /1 I 1 I //!ll////1//1/11/;/111 //1////////////1////// ////////////////////// //////////..-"..-"//..-"/////// /~/?~~~~~~~~~~~~~///~/
(b)
Figure 3. Direction of the magnetic field for a given phase angle on the y-z plane cross section through the ECS coil, target and profile line for (a) a target offset of zero and (b) a target offset of 0.6 times the sensor coil diameter. Note that the magnitude of the field
is not shown by this diagram.
The form of the field profiles may be understood in terms of the direction of the magnetic field vectors as illustrated by figures 3(a) and 3(b). Below the centre of the ECS coil the vectors are vertical (large z-component) as they are within the coil. Moving along the profile line away from the ECS coil centre the flux lines start to curve around and the vector takes on an increasing horizontal component. Immediately below the ECS coil edge the vector is horizontal (large y-component) and the there is a dip on the curves of figures 2(a) and 2(b). For the zero-offset geometry the z-component of the field increases as the flux lines sweep back up to join the upper end of the ECS coil. IBzl then drops off as the field decays with increasing displacement from the source. For the
94
Appendix 1
geometry with an offset of 0.6 times the ECS coil diameter there is also an initial increase as the flux sweeps back up, however in this case the target edge comes into play. Some of the flux lines are swept down and around the target so the field lines are spilt. This has the effect of creating more horizontal than vertical components of the field and thus IBzl decreases.
3. Experimental Confirmation
The modelling results were confirmed by measuring the magnetic field outside of the ECS coil with small tightly-wound test coils. These test coils were constructed from fine copper wire and an air core was used so as to minimise the disruption to the field. The stranded nature of the devices meant that eddy current interactions were small. An Agilent Technologies impedance analyser was used to match the natural frequency of the test coils closely to the 1 MHz of the ECS coil; this enabled maximum response and sensitivity. The test coils were connected to a digital oscilloscope and the amplitude of the signal recorded.
Two test coils were employed and were positioned either side of the ECS coil on the y-axis in figure 1 so as so track changes in the lobes of figure 2. The offset of the target material was increased and the output from the test coils was recorded. This has been expressed in normalised terms to highlight the variation from the zero-offset case. The ECS output was also recorded and was observed to change as the offset increased, even thought the actual target distance (d1) remained constant. This is expressed in terms of a percentage distance error, which is simply:
dr(en) -dr % distance error = · x 100
dr
where dt(ecs) is the distance given by the eddy current ECS. Figure 4 shows the normalised output of the test coil on the side of the
approaching target edge (i.e. positive y-axis position on figure 1) and the % distance error. For low values of the normalised ECS coil offset (:S0.6), the small distance errors were caused by experimental limitations and were not actual device errors.
'[ Test coil :; 0
~ 0.8 (.) ~ [/)
~ -o 0.6
<1)
.~ C<i E Ci 0.4 z
Distance error ---0.2 i=-'='--'=;-~=-r=-=-:-=-=-=--=-::;-=--=-=-=-=-::r-'----,---~----'-
0 0.2 0.4 0.6 0.8 1.2 Normalised sensor coil offset
12
10
8 ... 0 !: <1)
<1)
6 (.) c:: .::3 "'
4 :a ~
2
0
Figure 4. Graph showing percentage distance error resulting from target lateral displacement and the output from the test coil.
95
Appendix 1
When the ECS coil and target edges were aligned (an offset of 1 times the ECS diameter) there was a 6.5% error in the target distance as given by the ECS. The output of a test coil positioned at 1.3 times the ECS coil radius was found to be 0.47 of the value when the target was centred. Thus by monitoring the test coils in this way, it was possible to correct for the errors caused by target offset.
The direction of the target offset was also determined by comparing the output from the two test coils. As can be seen in figure 2 only the lobe closest to the approaching target edge was affected; the opposite lobe remained static.
4. Condusions
This paper has demonstrated by using finite element field simulations that there is more information available from the ECS system than is extracted by only measuring the impedance of the ECS coil. Outside the ECS coil lobes were observed in the zcomponent of the magnitude of the magnetic field. As the offset of the target material was increased the lobe on the side of the advancing target edge was observed to decrease in magnitude and its lateral extension was curtailed. By monitoring small test coils positioned to observe these lobes it was possible to counteract the effect on the ECS coil.
With further work the system of test coils and the ECS coil could be combined into a package that was resistant the harsh environment in which ECSs are often employed. The signal from the test coil could be monitored by an electronic system that could directly modify the output from the ECS device. This would make an eddy current distance measuring device that could be used in situations where the target materials were not always centred. Such applications include environments targets move through the path of the ECS (e.g. production lines) and where the target may be knocked out of alignment (e.g. rolling mills).
Acknowledgements
This work is supported by funding from the UK EPSRC reference number GR/R58475/0l.
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